1536750489.510 * [misc]progress: [Phase 1 of 3] Setting up. 1536750489.510 * * * [misc]progress: [1/2] Preparing points 1536750489.511 * * * * [misc]points: Sampling 256 additional inputs, on iter 0 have 0 / 256 1536750489.513 * * * * [misc]points: Computing exacts on every 16 of 256 points to ramp up precision 1536750489.518 * * * * [misc]points: Setting MPFR precision to 64 1536750489.520 * * * * [misc]points: Setting MPFR precision to 320 1536750489.522 * * * * [misc]points: Setting MPFR precision to 576 1536750489.523 * * * * [misc]points: Computing exacts on every 8 of 256 points to ramp up precision 1536750489.533 * * * * [misc]points: Setting MPFR precision to 320 1536750489.536 * * * * [misc]points: Setting MPFR precision to 576 1536750489.539 * * * * [misc]points: Setting MPFR precision to 832 1536750489.541 * * * * [misc]points: Computing exacts on every 4 of 256 points to ramp up precision 1536750489.547 * * * * [misc]points: Setting MPFR precision to 576 1536750489.549 * * * * [misc]points: Setting MPFR precision to 832 1536750489.557 * * * * [misc]points: Setting MPFR precision to 1088 1536750489.560 * * * * [misc]points: Setting MPFR precision to 1344 1536750489.563 * * * * [misc]points: Computing exacts on every 2 of 256 points to ramp up precision 1536750489.578 * * * * [misc]points: Setting MPFR precision to 1088 1536750489.587 * * * * [misc]points: Setting MPFR precision to 1344 1536750489.596 * * * * [misc]points: Computing exacts for 256 points 1536750489.615 * * * * [misc]points: Setting MPFR precision to 1088 1536750489.643 * * * * [misc]points: Setting MPFR precision to 1344 1536750489.671 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750489.672 * * * * [misc]points: Sampling 207 additional inputs, on iter 1 have 49 / 256 1536750489.673 * * * * [misc]points: Computing exacts on every 12 of 207 points to ramp up precision 1536750489.695 * * * * [misc]points: Setting MPFR precision to 1088 1536750489.696 * * * * [misc]points: Setting MPFR precision to 1344 1536750489.698 * * * * [misc]points: Computing exacts on every 6 of 207 points to ramp up precision 1536750489.710 * * * * [misc]points: Setting MPFR precision to 1088 1536750489.713 * * * * [misc]points: Setting MPFR precision to 1344 1536750489.716 * * * * [misc]points: Computing exacts on every 3 of 207 points to ramp up precision 1536750489.740 * * * * [misc]points: Setting MPFR precision to 1088 1536750489.746 * * * * [misc]points: Setting MPFR precision to 1344 1536750489.753 * * * * [misc]points: Computing exacts for 207 points 1536750489.772 * * * * [misc]points: Setting MPFR precision to 1088 1536750489.792 * * * * [misc]points: Setting MPFR precision to 1344 1536750489.804 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750489.804 * * * * [misc]points: Sampling 164 additional inputs, on iter 2 have 92 / 256 1536750489.805 * * * * [misc]points: Computing exacts on every 10 of 164 points to ramp up precision 1536750489.814 * * * * [misc]points: Setting MPFR precision to 1088 1536750489.815 * * * * [misc]points: Setting MPFR precision to 1344 1536750489.816 * * * * [misc]points: Computing exacts on every 5 of 164 points to ramp up precision 1536750489.848 * * * * [misc]points: Setting MPFR precision to 1088 1536750489.851 * * * * [misc]points: Setting MPFR precision to 1344 1536750489.854 * * * * [misc]points: Computing exacts on every 2 of 164 points to ramp up precision 1536750489.872 * * * * [misc]points: Setting MPFR precision to 1088 1536750489.877 * * * * [misc]points: Setting MPFR precision to 1344 1536750489.883 * * * * [misc]points: Computing exacts for 164 points 1536750489.901 * * * * [misc]points: Setting MPFR precision to 1088 1536750489.916 * * * * [misc]points: Setting MPFR precision to 1344 1536750489.925 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750489.925 * * * * [misc]points: Sampling 137 additional inputs, on iter 3 have 119 / 256 1536750489.926 * * * * [misc]points: Computing exacts on every 8 of 137 points to ramp up precision 1536750489.935 * * * * [misc]points: Setting MPFR precision to 1088 1536750489.936 * * * * [misc]points: Setting MPFR precision to 1344 1536750489.937 * * * * [misc]points: Computing exacts on every 4 of 137 points to ramp up precision 1536750489.951 * * * * [misc]points: Setting MPFR precision to 1088 1536750489.954 * * * * [misc]points: Setting MPFR precision to 1344 1536750489.957 * * * * [misc]points: Computing exacts on every 2 of 137 points to ramp up precision 1536750489.982 * * * * [misc]points: Setting MPFR precision to 1088 1536750489.988 * * * * [misc]points: Setting MPFR precision to 1344 1536750489.992 * * * * [misc]points: Computing exacts for 137 points 1536750490.010 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.023 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.038 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.038 * * * * [misc]points: Sampling 114 additional inputs, on iter 4 have 142 / 256 1536750490.039 * * * * [misc]points: Computing exacts on every 7 of 114 points to ramp up precision 1536750490.050 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.051 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.052 * * * * [misc]points: Computing exacts on every 3 of 114 points to ramp up precision 1536750490.070 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.072 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.073 * * * * [misc]points: Computing exacts for 114 points 1536750490.082 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.088 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.099 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.099 * * * * [misc]points: Sampling 89 additional inputs, on iter 5 have 167 / 256 1536750490.100 * * * * [misc]points: Computing exacts on every 5 of 89 points to ramp up precision 1536750490.125 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.127 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.129 * * * * [misc]points: Computing exacts on every 2 of 89 points to ramp up precision 1536750490.148 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.152 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.155 * * * * [misc]points: Computing exacts for 89 points 1536750490.173 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.182 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.191 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.191 * * * * [misc]points: Sampling 75 additional inputs, on iter 6 have 181 / 256 1536750490.191 * * * * [misc]points: Computing exacts on every 4 of 75 points to ramp up precision 1536750490.216 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.217 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.218 * * * * [misc]points: Computing exacts on every 2 of 75 points to ramp up precision 1536750490.234 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.237 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.239 * * * * [misc]points: Computing exacts for 75 points 1536750490.255 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.262 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.269 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.269 * * * * [misc]points: Sampling 64 additional inputs, on iter 7 have 192 / 256 1536750490.270 * * * * [misc]points: Computing exacts on every 4 of 64 points to ramp up precision 1536750490.286 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.287 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.288 * * * * [misc]points: Computing exacts on every 2 of 64 points to ramp up precision 1536750490.296 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.298 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.299 * * * * [misc]points: Computing exacts for 64 points 1536750490.307 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.313 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.320 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.320 * * * * [misc]points: Sampling 55 additional inputs, on iter 8 have 201 / 256 1536750490.321 * * * * [misc]points: Computing exacts on every 3 of 55 points to ramp up precision 1536750490.345 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.347 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.348 * * * * [misc]points: Computing exacts for 55 points 1536750490.365 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.368 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.372 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.372 * * * * [misc]points: Sampling 45 additional inputs, on iter 9 have 211 / 256 1536750490.372 * * * * [misc]points: Computing exacts on every 2 of 45 points to ramp up precision 1536750490.384 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.385 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.386 * * * * [misc]points: Computing exacts for 45 points 1536750490.399 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.403 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.408 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.408 * * * * [misc]points: Sampling 37 additional inputs, on iter 10 have 219 / 256 1536750490.408 * * * * [misc]points: Computing exacts on every 2 of 37 points to ramp up precision 1536750490.426 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.428 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.429 * * * * [misc]points: Computing exacts for 37 points 1536750490.453 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.455 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.457 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.457 * * * * [misc]points: Sampling 31 additional inputs, on iter 11 have 225 / 256 1536750490.457 * * * * [misc]points: Computing exacts for 31 points 1536750490.466 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.468 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.469 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.469 * * * * [misc]points: Sampling 26 additional inputs, on iter 12 have 230 / 256 1536750490.469 * * * * [misc]points: Computing exacts for 26 points 1536750490.478 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.480 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.482 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.482 * * * * [misc]points: Sampling 22 additional inputs, on iter 13 have 234 / 256 1536750490.482 * * * * [misc]points: Computing exacts for 22 points 1536750490.501 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.505 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.507 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.507 * * * * [misc]points: Sampling 15 additional inputs, on iter 14 have 241 / 256 1536750490.508 * * * * [misc]points: Computing exacts for 15 points 1536750490.522 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.523 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.524 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.524 * * * * [misc]points: Sampling 11 additional inputs, on iter 15 have 245 / 256 1536750490.524 * * * * [misc]points: Computing exacts for 11 points 1536750490.533 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.534 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.534 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.534 * * * * [misc]points: Sampling 11 additional inputs, on iter 16 have 245 / 256 1536750490.534 * * * * [misc]points: Computing exacts for 11 points 1536750490.546 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.547 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.548 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.548 * * * * [misc]points: Sampling 11 additional inputs, on iter 17 have 245 / 256 1536750490.548 * * * * [misc]points: Computing exacts for 11 points 1536750490.560 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.561 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.562 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.562 * * * * [misc]points: Sampling 9 additional inputs, on iter 18 have 247 / 256 1536750490.562 * * * * [misc]points: Computing exacts for 9 points 1536750490.570 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.571 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.572 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.572 * * * * [misc]points: Sampling 8 additional inputs, on iter 19 have 248 / 256 1536750490.572 * * * * [misc]points: Computing exacts for 8 points 1536750490.584 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.585 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.586 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.586 * * * * [misc]points: Sampling 6 additional inputs, on iter 20 have 250 / 256 1536750490.586 * * * * [misc]points: Computing exacts for 6 points 1536750490.604 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.604 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.605 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.605 * * * * [misc]points: Sampling 5 additional inputs, on iter 21 have 251 / 256 1536750490.605 * * * * [misc]points: Computing exacts for 5 points 1536750490.621 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.622 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.622 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.622 * * * * [misc]points: Sampling 5 additional inputs, on iter 22 have 251 / 256 1536750490.622 * * * * [misc]points: Computing exacts for 5 points 1536750490.633 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.634 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.634 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.634 * * * * [misc]points: Sampling 5 additional inputs, on iter 23 have 251 / 256 1536750490.634 * * * * [misc]points: Computing exacts for 5 points 1536750490.642 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.643 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.643 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.643 * * * * [misc]points: Sampling 4 additional inputs, on iter 24 have 252 / 256 1536750490.643 * * * * [misc]points: Computing exacts for 4 points 1536750490.657 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.658 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.658 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.658 * * * * [misc]points: Sampling 4 additional inputs, on iter 25 have 253 / 256 1536750490.658 * * * * [misc]points: Computing exacts for 4 points 1536750490.676 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.676 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.676 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.676 * * * * [misc]points: Sampling 4 additional inputs, on iter 26 have 253 / 256 1536750490.676 * * * * [misc]points: Computing exacts for 4 points 1536750490.685 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.685 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.686 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.686 * * * * [misc]points: Sampling 4 additional inputs, on iter 27 have 254 / 256 1536750490.686 * * * * [misc]points: Computing exacts for 4 points 1536750490.697 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.698 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.698 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.698 * * * * [misc]points: Sampling 4 additional inputs, on iter 28 have 255 / 256 1536750490.698 * * * * [misc]points: Computing exacts for 4 points 1536750490.718 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.718 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.719 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.719 * * * * [misc]points: Sampling 4 additional inputs, on iter 29 have 255 / 256 1536750490.719 * * * * [misc]points: Computing exacts for 4 points 1536750490.728 * * * * [misc]points: Setting MPFR precision to 1088 1536750490.728 * * * * [misc]points: Setting MPFR precision to 1344 1536750490.729 * * * * [misc]points: Filtering points with unrepresentable outputs 1536750490.729 * * * * [exit]points: Sampled 256 points with exact outputs 1536750490.729 * * * [misc]progress: [2/2] Setting up program. 1536750490.735 * [misc]progress: [Phase 2 of 3] Improving. 1536750490.735 * [enter]simplify: Simplifying (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1536750490.736 * * [misc]simplify: iters left: 6 (13 enodes) 1536750490.740 * * [misc]simplify: iters left: 5 (28 enodes) 1536750490.746 * * [misc]simplify: iters left: 4 (44 enodes) 1536750490.761 * * [misc]simplify: iters left: 3 (54 enodes) 1536750490.774 * * [misc]simplify: iters left: 2 (57 enodes) 1536750490.788 * * [misc]simplify: iters left: 1 (65 enodes) 1536750490.813 * [exit]simplify: Simplified to (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1536750490.833 * * [misc]progress: iteration 1 / 4 1536750490.833 * * * [misc]progress: picking best candidate 1536750490.853 * * * * [misc]pick: Picked # 1536750490.853 * * * [misc]progress: localizing error 1536750490.899 * * * [misc]progress: generating rewritten candidates 1536750490.899 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1536750490.931 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1) 1536750490.949 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1536750490.995 * * * [misc]progress: generating series expansions 1536750490.995 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1536750490.995 * [misc]backup-simplify: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1536750490.995 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1536750490.995 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1536750490.995 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1536750490.995 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1536750490.995 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750490.995 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750490.995 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750490.995 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750490.995 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750490.995 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750490.995 * [misc]taylor: Taking taylor expansion of k in k 1536750490.995 * [misc]backup-simplify: Simplify 0 into 0 1536750490.995 * [misc]backup-simplify: Simplify 1 into 1 1536750490.995 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1536750490.995 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1536750490.995 * [misc]taylor: Taking taylor expansion of 2 in k 1536750490.995 * [misc]backup-simplify: Simplify 2 into 2 1536750490.995 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536750490.995 * [misc]taylor: Taking taylor expansion of n in k 1536750490.995 * [misc]backup-simplify: Simplify n into n 1536750490.995 * [misc]taylor: Taking taylor expansion of PI in k 1536750490.995 * [misc]backup-simplify: Simplify PI into PI 1536750490.995 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536750490.995 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1536750490.996 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1536750490.996 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750490.996 * [misc]backup-simplify: Simplify (- 0) into 0 1536750490.996 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750490.996 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1536750490.996 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1536750490.996 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536750490.996 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536750490.996 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536750490.996 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750490.996 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750490.996 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750490.996 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750490.996 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750490.996 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750490.996 * [misc]taylor: Taking taylor expansion of k in n 1536750490.996 * [misc]backup-simplify: Simplify k into k 1536750490.996 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536750490.997 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536750490.997 * [misc]taylor: Taking taylor expansion of 2 in n 1536750490.997 * [misc]backup-simplify: Simplify 2 into 2 1536750490.997 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750490.997 * [misc]taylor: Taking taylor expansion of n in n 1536750490.997 * [misc]backup-simplify: Simplify 0 into 0 1536750490.997 * [misc]backup-simplify: Simplify 1 into 1 1536750490.997 * [misc]taylor: Taking taylor expansion of PI in n 1536750490.997 * [misc]backup-simplify: Simplify PI into PI 1536750490.997 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750490.997 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536750490.997 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750490.998 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536750490.998 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750490.998 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750490.998 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750490.998 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750490.999 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750490.999 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1536750491.000 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1536750491.000 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536750491.000 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536750491.000 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536750491.000 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750491.000 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.000 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.000 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750491.000 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.000 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.000 * [misc]taylor: Taking taylor expansion of k in n 1536750491.000 * [misc]backup-simplify: Simplify k into k 1536750491.000 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536750491.000 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536750491.000 * [misc]taylor: Taking taylor expansion of 2 in n 1536750491.000 * [misc]backup-simplify: Simplify 2 into 2 1536750491.000 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750491.000 * [misc]taylor: Taking taylor expansion of n in n 1536750491.000 * [misc]backup-simplify: Simplify 0 into 0 1536750491.000 * [misc]backup-simplify: Simplify 1 into 1 1536750491.000 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.000 * [misc]backup-simplify: Simplify PI into PI 1536750491.000 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750491.000 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536750491.001 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750491.001 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536750491.002 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750491.002 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750491.002 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750491.002 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750491.002 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750491.003 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1536750491.003 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1536750491.003 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1536750491.003 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1536750491.003 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750491.003 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.003 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.003 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750491.003 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.003 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.003 * [misc]taylor: Taking taylor expansion of k in k 1536750491.003 * [misc]backup-simplify: Simplify 0 into 0 1536750491.003 * [misc]backup-simplify: Simplify 1 into 1 1536750491.004 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536750491.004 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750491.004 * [misc]taylor: Taking taylor expansion of n in k 1536750491.004 * [misc]backup-simplify: Simplify n into n 1536750491.004 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750491.004 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536750491.004 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536750491.004 * [misc]taylor: Taking taylor expansion of 2 in k 1536750491.004 * [misc]backup-simplify: Simplify 2 into 2 1536750491.004 * [misc]taylor: Taking taylor expansion of PI in k 1536750491.004 * [misc]backup-simplify: Simplify PI into PI 1536750491.004 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750491.004 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750491.004 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750491.004 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.005 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750491.005 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750491.005 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1536750491.006 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1536750491.006 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1536750491.007 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536750491.008 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536750491.009 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536750491.010 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536750491.010 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.010 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.010 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750491.011 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1536750491.012 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750491.012 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.012 * [misc]backup-simplify: Simplify 0 into 0 1536750491.012 * [misc]backup-simplify: Simplify 0 into 0 1536750491.013 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536750491.013 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536750491.015 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536750491.015 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.015 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536750491.015 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750491.015 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750491.017 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1536750491.019 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536750491.020 * [misc]backup-simplify: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536750491.022 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750491.024 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536750491.030 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536750491.030 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536750491.030 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.031 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.031 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750491.032 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536750491.034 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750491.034 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.034 * [misc]backup-simplify: Simplify 0 into 0 1536750491.034 * [misc]backup-simplify: Simplify 0 into 0 1536750491.034 * [misc]backup-simplify: Simplify 0 into 0 1536750491.038 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536750491.039 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536750491.043 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536750491.043 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.043 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536750491.043 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.043 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.044 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536750491.046 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1536750491.049 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1536750491.055 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1536750491.055 * [misc]backup-simplify: Simplify (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536750491.055 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1536750491.055 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750491.056 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1536750491.056 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1536750491.056 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750491.056 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.056 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.056 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750491.056 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.056 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.056 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750491.056 * [misc]taylor: Taking taylor expansion of k in k 1536750491.056 * [misc]backup-simplify: Simplify 0 into 0 1536750491.056 * [misc]backup-simplify: Simplify 1 into 1 1536750491.056 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750491.056 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1536750491.056 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1536750491.056 * [misc]taylor: Taking taylor expansion of 2 in k 1536750491.056 * [misc]backup-simplify: Simplify 2 into 2 1536750491.056 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750491.056 * [misc]taylor: Taking taylor expansion of PI in k 1536750491.056 * [misc]backup-simplify: Simplify PI into PI 1536750491.056 * [misc]taylor: Taking taylor expansion of n in k 1536750491.056 * [misc]backup-simplify: Simplify n into n 1536750491.056 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750491.056 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1536750491.056 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1536750491.056 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750491.057 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750491.057 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750491.057 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1536750491.057 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536750491.057 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750491.057 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536750491.057 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536750491.057 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750491.057 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.057 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.057 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750491.057 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.057 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.057 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750491.057 * [misc]taylor: Taking taylor expansion of k in n 1536750491.057 * [misc]backup-simplify: Simplify k into k 1536750491.057 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750491.057 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536750491.057 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536750491.057 * [misc]taylor: Taking taylor expansion of 2 in n 1536750491.057 * [misc]backup-simplify: Simplify 2 into 2 1536750491.057 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750491.057 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.057 * [misc]backup-simplify: Simplify PI into PI 1536750491.058 * [misc]taylor: Taking taylor expansion of n in n 1536750491.058 * [misc]backup-simplify: Simplify 0 into 0 1536750491.058 * [misc]backup-simplify: Simplify 1 into 1 1536750491.058 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750491.058 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750491.058 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750491.058 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750491.058 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750491.059 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750491.059 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750491.060 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1536750491.061 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536750491.061 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750491.061 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536750491.061 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536750491.061 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750491.061 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.061 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.061 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750491.061 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.061 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.061 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750491.061 * [misc]taylor: Taking taylor expansion of k in n 1536750491.061 * [misc]backup-simplify: Simplify k into k 1536750491.061 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750491.061 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536750491.061 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536750491.061 * [misc]taylor: Taking taylor expansion of 2 in n 1536750491.061 * [misc]backup-simplify: Simplify 2 into 2 1536750491.061 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750491.061 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.061 * [misc]backup-simplify: Simplify PI into PI 1536750491.061 * [misc]taylor: Taking taylor expansion of n in n 1536750491.061 * [misc]backup-simplify: Simplify 0 into 0 1536750491.061 * [misc]backup-simplify: Simplify 1 into 1 1536750491.061 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750491.061 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750491.062 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750491.062 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750491.062 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750491.062 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750491.062 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750491.063 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1536750491.063 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536750491.064 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1536750491.064 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1536750491.064 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750491.064 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.064 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.064 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750491.064 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.064 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.064 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750491.064 * [misc]taylor: Taking taylor expansion of k in k 1536750491.064 * [misc]backup-simplify: Simplify 0 into 0 1536750491.064 * [misc]backup-simplify: Simplify 1 into 1 1536750491.064 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750491.064 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536750491.064 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536750491.064 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536750491.064 * [misc]taylor: Taking taylor expansion of 2 in k 1536750491.064 * [misc]backup-simplify: Simplify 2 into 2 1536750491.064 * [misc]taylor: Taking taylor expansion of PI in k 1536750491.064 * [misc]backup-simplify: Simplify PI into PI 1536750491.064 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750491.065 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750491.065 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750491.065 * [misc]taylor: Taking taylor expansion of n in k 1536750491.065 * [misc]backup-simplify: Simplify n into n 1536750491.065 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750491.065 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750491.065 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750491.065 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750491.065 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536750491.065 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536750491.066 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536750491.067 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536750491.067 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536750491.068 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750491.068 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536750491.070 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536750491.071 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750491.071 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750491.071 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.071 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.072 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750491.072 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1536750491.073 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750491.073 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.073 * [misc]backup-simplify: Simplify 0 into 0 1536750491.073 * [misc]backup-simplify: Simplify 0 into 0 1536750491.073 * [misc]backup-simplify: Simplify 0 into 0 1536750491.074 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.075 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536750491.079 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536750491.079 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750491.079 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750491.079 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.079 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.080 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750491.080 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1536750491.082 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750491.082 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.082 * [misc]backup-simplify: Simplify 0 into 0 1536750491.082 * [misc]backup-simplify: Simplify 0 into 0 1536750491.082 * [misc]backup-simplify: Simplify 0 into 0 1536750491.082 * [misc]backup-simplify: Simplify 0 into 0 1536750491.083 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.084 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750491.090 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536750491.090 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750491.090 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536750491.090 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.090 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.091 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750491.092 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1536750491.096 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750491.096 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.096 * [misc]backup-simplify: Simplify 0 into 0 1536750491.096 * [misc]backup-simplify: Simplify 0 into 0 1536750491.097 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1536750491.097 * [misc]backup-simplify: Simplify (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750491.097 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1536750491.097 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750491.097 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1536750491.097 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1536750491.097 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750491.097 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750491.097 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.098 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.098 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750491.098 * [misc]taylor: Taking taylor expansion of k in k 1536750491.098 * [misc]backup-simplify: Simplify 0 into 0 1536750491.098 * [misc]backup-simplify: Simplify 1 into 1 1536750491.098 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750491.098 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.098 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.098 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1536750491.098 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536750491.098 * [misc]taylor: Taking taylor expansion of -2 in k 1536750491.098 * [misc]backup-simplify: Simplify -2 into -2 1536750491.098 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750491.098 * [misc]taylor: Taking taylor expansion of PI in k 1536750491.098 * [misc]backup-simplify: Simplify PI into PI 1536750491.098 * [misc]taylor: Taking taylor expansion of n in k 1536750491.098 * [misc]backup-simplify: Simplify n into n 1536750491.098 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750491.098 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536750491.098 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1536750491.099 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750491.099 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750491.099 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1536750491.099 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750491.099 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750491.099 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536750491.100 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536750491.100 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750491.100 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750491.100 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.100 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.100 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750491.100 * [misc]taylor: Taking taylor expansion of k in n 1536750491.100 * [misc]backup-simplify: Simplify k into k 1536750491.100 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750491.100 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.100 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.100 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536750491.100 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536750491.100 * [misc]taylor: Taking taylor expansion of -2 in n 1536750491.100 * [misc]backup-simplify: Simplify -2 into -2 1536750491.100 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750491.100 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.100 * [misc]backup-simplify: Simplify PI into PI 1536750491.100 * [misc]taylor: Taking taylor expansion of n in n 1536750491.100 * [misc]backup-simplify: Simplify 0 into 0 1536750491.100 * [misc]backup-simplify: Simplify 1 into 1 1536750491.101 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750491.101 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536750491.101 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536750491.102 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750491.102 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750491.102 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750491.103 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1536750491.104 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536750491.104 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750491.104 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536750491.104 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536750491.104 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750491.104 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750491.104 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.104 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.104 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750491.104 * [misc]taylor: Taking taylor expansion of k in n 1536750491.104 * [misc]backup-simplify: Simplify k into k 1536750491.104 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750491.104 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.104 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.104 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536750491.104 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536750491.104 * [misc]taylor: Taking taylor expansion of -2 in n 1536750491.104 * [misc]backup-simplify: Simplify -2 into -2 1536750491.104 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750491.105 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.105 * [misc]backup-simplify: Simplify PI into PI 1536750491.105 * [misc]taylor: Taking taylor expansion of n in n 1536750491.105 * [misc]backup-simplify: Simplify 0 into 0 1536750491.105 * [misc]backup-simplify: Simplify 1 into 1 1536750491.105 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750491.105 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536750491.106 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536750491.106 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750491.106 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750491.107 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750491.107 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1536750491.108 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536750491.108 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1536750491.108 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1536750491.108 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750491.108 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750491.108 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.108 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.108 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750491.108 * [misc]taylor: Taking taylor expansion of k in k 1536750491.109 * [misc]backup-simplify: Simplify 0 into 0 1536750491.109 * [misc]backup-simplify: Simplify 1 into 1 1536750491.109 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750491.109 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.109 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.109 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536750491.109 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536750491.109 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536750491.109 * [misc]taylor: Taking taylor expansion of -2 in k 1536750491.109 * [misc]backup-simplify: Simplify -2 into -2 1536750491.109 * [misc]taylor: Taking taylor expansion of PI in k 1536750491.109 * [misc]backup-simplify: Simplify PI into PI 1536750491.109 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536750491.110 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536750491.110 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750491.110 * [misc]taylor: Taking taylor expansion of n in k 1536750491.110 * [misc]backup-simplify: Simplify n into n 1536750491.110 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750491.110 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750491.110 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750491.110 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536750491.111 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536750491.112 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1536750491.112 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536750491.113 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536750491.114 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750491.115 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536750491.117 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1536750491.117 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750491.118 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750491.118 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.118 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750491.119 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1536750491.120 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750491.120 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.120 * [misc]backup-simplify: Simplify 0 into 0 1536750491.120 * [misc]backup-simplify: Simplify 0 into 0 1536750491.120 * [misc]backup-simplify: Simplify 0 into 0 1536750491.121 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.121 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536750491.125 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1536750491.125 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750491.125 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750491.125 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.126 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750491.126 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1536750491.128 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750491.128 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.128 * [misc]backup-simplify: Simplify 0 into 0 1536750491.128 * [misc]backup-simplify: Simplify 0 into 0 1536750491.128 * [misc]backup-simplify: Simplify 0 into 0 1536750491.128 * [misc]backup-simplify: Simplify 0 into 0 1536750491.129 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.130 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750491.136 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 1536750491.136 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750491.136 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536750491.136 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.137 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750491.138 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1536750491.140 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750491.140 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.140 * [misc]backup-simplify: Simplify 0 into 0 1536750491.140 * [misc]backup-simplify: Simplify 0 into 0 1536750491.141 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1536750491.141 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1) 1536750491.141 * [misc]backup-simplify: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 1536750491.141 * [misc]approximate: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1536750491.141 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536750491.141 * [misc]taylor: Taking taylor expansion of 2 in n 1536750491.141 * [misc]backup-simplify: Simplify 2 into 2 1536750491.141 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750491.141 * [misc]taylor: Taking taylor expansion of n in n 1536750491.141 * [misc]backup-simplify: Simplify 0 into 0 1536750491.141 * [misc]backup-simplify: Simplify 1 into 1 1536750491.141 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.141 * [misc]backup-simplify: Simplify PI into PI 1536750491.141 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536750491.141 * [misc]taylor: Taking taylor expansion of 2 in n 1536750491.141 * [misc]backup-simplify: Simplify 2 into 2 1536750491.141 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750491.141 * [misc]taylor: Taking taylor expansion of n in n 1536750491.141 * [misc]backup-simplify: Simplify 0 into 0 1536750491.141 * [misc]backup-simplify: Simplify 1 into 1 1536750491.141 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.141 * [misc]backup-simplify: Simplify PI into PI 1536750491.142 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750491.142 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536750491.142 * [misc]backup-simplify: Simplify 0 into 0 1536750491.142 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750491.143 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536750491.143 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750491.144 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536750491.145 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536750491.145 * [misc]backup-simplify: Simplify 0 into 0 1536750491.147 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750491.148 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536750491.148 * [misc]backup-simplify: Simplify 0 into 0 1536750491.151 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536750491.153 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536750491.153 * [misc]backup-simplify: Simplify 0 into 0 1536750491.159 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536750491.162 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1536750491.162 * [misc]backup-simplify: Simplify 0 into 0 1536750491.166 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536750491.170 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1536750491.170 * [misc]backup-simplify: Simplify 0 into 0 1536750491.174 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1536750491.179 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1536750491.179 * [misc]backup-simplify: Simplify 0 into 0 1536750491.179 * [misc]backup-simplify: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 1536750491.180 * [misc]backup-simplify: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 1536750491.180 * [misc]approximate: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1536750491.180 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536750491.180 * [misc]taylor: Taking taylor expansion of 2 in n 1536750491.180 * [misc]backup-simplify: Simplify 2 into 2 1536750491.180 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750491.180 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.180 * [misc]backup-simplify: Simplify PI into PI 1536750491.180 * [misc]taylor: Taking taylor expansion of n in n 1536750491.180 * [misc]backup-simplify: Simplify 0 into 0 1536750491.180 * [misc]backup-simplify: Simplify 1 into 1 1536750491.180 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750491.180 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536750491.180 * [misc]taylor: Taking taylor expansion of 2 in n 1536750491.180 * [misc]backup-simplify: Simplify 2 into 2 1536750491.180 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750491.180 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.180 * [misc]backup-simplify: Simplify PI into PI 1536750491.180 * [misc]taylor: Taking taylor expansion of n in n 1536750491.180 * [misc]backup-simplify: Simplify 0 into 0 1536750491.181 * [misc]backup-simplify: Simplify 1 into 1 1536750491.181 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750491.181 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750491.181 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750491.183 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750491.183 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536750491.183 * [misc]backup-simplify: Simplify 0 into 0 1536750491.185 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.186 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536750491.186 * [misc]backup-simplify: Simplify 0 into 0 1536750491.188 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.189 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750491.189 * [misc]backup-simplify: Simplify 0 into 0 1536750491.191 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.194 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536750491.194 * [misc]backup-simplify: Simplify 0 into 0 1536750491.196 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.199 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536750491.199 * [misc]backup-simplify: Simplify 0 into 0 1536750491.202 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.205 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536750491.205 * [misc]backup-simplify: Simplify 0 into 0 1536750491.206 * [misc]backup-simplify: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 1536750491.206 * [misc]backup-simplify: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 1536750491.206 * [misc]approximate: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1536750491.206 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536750491.206 * [misc]taylor: Taking taylor expansion of -2 in n 1536750491.206 * [misc]backup-simplify: Simplify -2 into -2 1536750491.206 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750491.206 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.206 * [misc]backup-simplify: Simplify PI into PI 1536750491.206 * [misc]taylor: Taking taylor expansion of n in n 1536750491.206 * [misc]backup-simplify: Simplify 0 into 0 1536750491.206 * [misc]backup-simplify: Simplify 1 into 1 1536750491.207 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750491.207 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536750491.207 * [misc]taylor: Taking taylor expansion of -2 in n 1536750491.207 * [misc]backup-simplify: Simplify -2 into -2 1536750491.207 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750491.207 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.207 * [misc]backup-simplify: Simplify PI into PI 1536750491.207 * [misc]taylor: Taking taylor expansion of n in n 1536750491.207 * [misc]backup-simplify: Simplify 0 into 0 1536750491.207 * [misc]backup-simplify: Simplify 1 into 1 1536750491.207 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750491.208 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536750491.208 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536750491.209 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750491.210 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536750491.210 * [misc]backup-simplify: Simplify 0 into 0 1536750491.211 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.212 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536750491.212 * [misc]backup-simplify: Simplify 0 into 0 1536750491.214 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.216 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750491.216 * [misc]backup-simplify: Simplify 0 into 0 1536750491.218 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.220 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536750491.220 * [misc]backup-simplify: Simplify 0 into 0 1536750491.223 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.226 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536750491.226 * [misc]backup-simplify: Simplify 0 into 0 1536750491.229 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.233 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536750491.233 * [misc]backup-simplify: Simplify 0 into 0 1536750491.233 * [misc]backup-simplify: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 1536750491.233 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1536750491.234 * [misc]backup-simplify: Simplify (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1536750491.234 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1536750491.234 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1536750491.234 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536750491.234 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750491.234 * [misc]taylor: Taking taylor expansion of k in k 1536750491.234 * [misc]backup-simplify: Simplify 0 into 0 1536750491.234 * [misc]backup-simplify: Simplify 1 into 1 1536750491.235 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750491.235 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750491.235 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750491.235 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1536750491.235 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1536750491.235 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1536750491.235 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750491.235 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.235 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.235 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750491.236 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.236 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.236 * [misc]taylor: Taking taylor expansion of k in k 1536750491.236 * [misc]backup-simplify: Simplify 0 into 0 1536750491.236 * [misc]backup-simplify: Simplify 1 into 1 1536750491.236 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1536750491.236 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1536750491.236 * [misc]taylor: Taking taylor expansion of 2 in k 1536750491.236 * [misc]backup-simplify: Simplify 2 into 2 1536750491.236 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536750491.236 * [misc]taylor: Taking taylor expansion of n in k 1536750491.236 * [misc]backup-simplify: Simplify n into n 1536750491.236 * [misc]taylor: Taking taylor expansion of PI in k 1536750491.236 * [misc]backup-simplify: Simplify PI into PI 1536750491.236 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536750491.236 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1536750491.236 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1536750491.237 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750491.237 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.237 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750491.237 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1536750491.237 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1536750491.237 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1536750491.237 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536750491.237 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750491.237 * [misc]taylor: Taking taylor expansion of k in n 1536750491.237 * [misc]backup-simplify: Simplify k into k 1536750491.237 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750491.237 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536750491.237 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750491.238 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536750491.238 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536750491.238 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536750491.238 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536750491.238 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750491.238 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.238 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.238 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750491.238 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.238 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.238 * [misc]taylor: Taking taylor expansion of k in n 1536750491.238 * [misc]backup-simplify: Simplify k into k 1536750491.238 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536750491.238 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536750491.238 * [misc]taylor: Taking taylor expansion of 2 in n 1536750491.238 * [misc]backup-simplify: Simplify 2 into 2 1536750491.238 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750491.238 * [misc]taylor: Taking taylor expansion of n in n 1536750491.238 * [misc]backup-simplify: Simplify 0 into 0 1536750491.238 * [misc]backup-simplify: Simplify 1 into 1 1536750491.238 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.238 * [misc]backup-simplify: Simplify PI into PI 1536750491.238 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750491.238 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536750491.239 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750491.239 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536750491.239 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750491.239 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750491.240 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750491.240 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750491.240 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750491.241 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1536750491.241 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1536750491.241 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1536750491.241 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536750491.241 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750491.241 * [misc]taylor: Taking taylor expansion of k in n 1536750491.241 * [misc]backup-simplify: Simplify k into k 1536750491.241 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750491.241 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536750491.241 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750491.241 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536750491.241 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536750491.241 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536750491.241 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536750491.241 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750491.241 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.241 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.241 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750491.241 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.241 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.241 * [misc]taylor: Taking taylor expansion of k in n 1536750491.241 * [misc]backup-simplify: Simplify k into k 1536750491.242 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536750491.242 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536750491.242 * [misc]taylor: Taking taylor expansion of 2 in n 1536750491.242 * [misc]backup-simplify: Simplify 2 into 2 1536750491.242 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750491.242 * [misc]taylor: Taking taylor expansion of n in n 1536750491.242 * [misc]backup-simplify: Simplify 0 into 0 1536750491.242 * [misc]backup-simplify: Simplify 1 into 1 1536750491.242 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.242 * [misc]backup-simplify: Simplify PI into PI 1536750491.242 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750491.242 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536750491.242 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750491.243 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536750491.243 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750491.243 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750491.243 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750491.243 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750491.244 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750491.244 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1536750491.245 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1536750491.245 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) 1536750491.245 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1536750491.245 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1536750491.245 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1536750491.245 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750491.245 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.245 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.245 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750491.245 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.245 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.245 * [misc]taylor: Taking taylor expansion of k in k 1536750491.245 * [misc]backup-simplify: Simplify 0 into 0 1536750491.245 * [misc]backup-simplify: Simplify 1 into 1 1536750491.246 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536750491.246 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750491.246 * [misc]taylor: Taking taylor expansion of n in k 1536750491.246 * [misc]backup-simplify: Simplify n into n 1536750491.246 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750491.246 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536750491.246 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536750491.246 * [misc]taylor: Taking taylor expansion of 2 in k 1536750491.246 * [misc]backup-simplify: Simplify 2 into 2 1536750491.246 * [misc]taylor: Taking taylor expansion of PI in k 1536750491.246 * [misc]backup-simplify: Simplify PI into PI 1536750491.246 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750491.246 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750491.246 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750491.246 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.247 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750491.247 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750491.247 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1536750491.248 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1536750491.248 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536750491.248 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750491.248 * [misc]taylor: Taking taylor expansion of k in k 1536750491.248 * [misc]backup-simplify: Simplify 0 into 0 1536750491.248 * [misc]backup-simplify: Simplify 1 into 1 1536750491.248 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750491.248 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750491.248 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750491.249 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1536750491.249 * [misc]backup-simplify: Simplify 0 into 0 1536750491.250 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536750491.250 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536750491.252 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536750491.252 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536750491.252 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.252 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.253 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750491.253 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1536750491.254 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750491.255 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1536750491.255 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.255 * [misc]backup-simplify: Simplify 0 into 0 1536750491.256 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536750491.256 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536750491.258 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536750491.258 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.258 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536750491.258 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750491.258 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750491.259 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1536750491.260 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536750491.262 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536750491.262 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536750491.263 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750491.264 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536750491.268 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536750491.268 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536750491.268 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.268 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.269 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750491.270 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536750491.272 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750491.273 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750491.273 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1536750491.274 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1536750491.274 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.275 * [misc]backup-simplify: Simplify 0 into 0 1536750491.275 * [misc]backup-simplify: Simplify 0 into 0 1536750491.275 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536750491.276 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750491.278 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536750491.279 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536750491.285 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536750491.285 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.286 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536750491.286 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.286 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.287 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536750491.290 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1536750491.300 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 1536750491.303 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 1536750491.306 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536750491.308 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536750491.317 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536750491.318 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1536750491.318 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.319 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.319 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750491.320 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1536750491.324 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750491.324 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750491.325 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1536750491.326 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 1536750491.326 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.326 * [misc]backup-simplify: Simplify 0 into 0 1536750491.326 * [misc]backup-simplify: Simplify 0 into 0 1536750491.326 * [misc]backup-simplify: Simplify 0 into 0 1536750491.327 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.328 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750491.332 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 1536750491.333 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750491.343 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536750491.343 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.343 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536750491.343 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.344 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.345 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1536750491.352 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536750491.371 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 1536750491.385 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 1536750491.404 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 1536750491.404 * [misc]backup-simplify: Simplify (/ (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536750491.404 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1536750491.404 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536750491.404 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536750491.405 * [misc]taylor: Taking taylor expansion of k in k 1536750491.405 * [misc]backup-simplify: Simplify 0 into 0 1536750491.405 * [misc]backup-simplify: Simplify 1 into 1 1536750491.405 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750491.405 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750491.405 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750491.405 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1536750491.405 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1536750491.405 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750491.405 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.405 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.405 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750491.406 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.406 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.406 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750491.406 * [misc]taylor: Taking taylor expansion of k in k 1536750491.406 * [misc]backup-simplify: Simplify 0 into 0 1536750491.406 * [misc]backup-simplify: Simplify 1 into 1 1536750491.406 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750491.406 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1536750491.406 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1536750491.406 * [misc]taylor: Taking taylor expansion of 2 in k 1536750491.406 * [misc]backup-simplify: Simplify 2 into 2 1536750491.406 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750491.406 * [misc]taylor: Taking taylor expansion of PI in k 1536750491.406 * [misc]backup-simplify: Simplify PI into PI 1536750491.406 * [misc]taylor: Taking taylor expansion of n in k 1536750491.406 * [misc]backup-simplify: Simplify n into n 1536750491.406 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750491.406 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1536750491.406 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1536750491.407 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750491.407 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750491.407 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750491.407 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1536750491.407 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536750491.408 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750491.408 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536750491.408 * [misc]taylor: Taking taylor expansion of k in n 1536750491.408 * [misc]backup-simplify: Simplify k into k 1536750491.408 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536750491.408 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536750491.408 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750491.408 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536750491.408 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536750491.408 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750491.408 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.408 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.408 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750491.408 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.408 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.408 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750491.408 * [misc]taylor: Taking taylor expansion of k in n 1536750491.408 * [misc]backup-simplify: Simplify k into k 1536750491.408 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750491.408 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536750491.408 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536750491.408 * [misc]taylor: Taking taylor expansion of 2 in n 1536750491.408 * [misc]backup-simplify: Simplify 2 into 2 1536750491.408 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750491.408 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.408 * [misc]backup-simplify: Simplify PI into PI 1536750491.408 * [misc]taylor: Taking taylor expansion of n in n 1536750491.408 * [misc]backup-simplify: Simplify 0 into 0 1536750491.409 * [misc]backup-simplify: Simplify 1 into 1 1536750491.409 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750491.409 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750491.410 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750491.410 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750491.410 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750491.410 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750491.411 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750491.411 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1536750491.412 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536750491.412 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750491.412 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536750491.412 * [misc]taylor: Taking taylor expansion of k in n 1536750491.412 * [misc]backup-simplify: Simplify k into k 1536750491.412 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536750491.413 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536750491.413 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750491.413 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536750491.413 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536750491.413 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750491.413 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.413 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.413 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750491.413 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.413 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.413 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750491.413 * [misc]taylor: Taking taylor expansion of k in n 1536750491.413 * [misc]backup-simplify: Simplify k into k 1536750491.413 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750491.413 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536750491.413 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536750491.413 * [misc]taylor: Taking taylor expansion of 2 in n 1536750491.413 * [misc]backup-simplify: Simplify 2 into 2 1536750491.413 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750491.413 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.413 * [misc]backup-simplify: Simplify PI into PI 1536750491.413 * [misc]taylor: Taking taylor expansion of n in n 1536750491.413 * [misc]backup-simplify: Simplify 0 into 0 1536750491.413 * [misc]backup-simplify: Simplify 1 into 1 1536750491.414 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750491.414 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750491.414 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750491.414 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750491.415 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750491.415 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750491.415 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750491.416 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1536750491.417 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536750491.418 * [misc]backup-simplify: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) 1536750491.418 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1536750491.418 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1536750491.418 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1536750491.418 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750491.418 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.418 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.418 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750491.418 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.418 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.418 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750491.418 * [misc]taylor: Taking taylor expansion of k in k 1536750491.418 * [misc]backup-simplify: Simplify 0 into 0 1536750491.418 * [misc]backup-simplify: Simplify 1 into 1 1536750491.418 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750491.418 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536750491.418 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536750491.418 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536750491.418 * [misc]taylor: Taking taylor expansion of 2 in k 1536750491.419 * [misc]backup-simplify: Simplify 2 into 2 1536750491.419 * [misc]taylor: Taking taylor expansion of PI in k 1536750491.419 * [misc]backup-simplify: Simplify PI into PI 1536750491.419 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750491.419 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750491.419 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750491.419 * [misc]taylor: Taking taylor expansion of n in k 1536750491.420 * [misc]backup-simplify: Simplify n into n 1536750491.420 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750491.420 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750491.420 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750491.420 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750491.420 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536750491.421 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536750491.421 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536750491.422 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536750491.422 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536750491.422 * [misc]taylor: Taking taylor expansion of k in k 1536750491.422 * [misc]backup-simplify: Simplify 0 into 0 1536750491.422 * [misc]backup-simplify: Simplify 1 into 1 1536750491.422 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750491.423 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750491.424 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1536750491.424 * [misc]backup-simplify: Simplify 0 into 0 1536750491.425 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750491.426 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536750491.429 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536750491.430 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750491.430 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750491.430 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.430 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.431 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750491.432 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1536750491.433 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750491.434 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1536750491.434 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.434 * [misc]backup-simplify: Simplify 0 into 0 1536750491.434 * [misc]backup-simplify: Simplify 0 into 0 1536750491.436 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536750491.436 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536750491.438 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.439 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536750491.445 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536750491.445 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750491.446 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750491.446 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.446 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.447 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750491.448 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1536750491.450 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750491.451 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1536750491.452 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1536750491.452 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.452 * [misc]backup-simplify: Simplify 0 into 0 1536750491.452 * [misc]backup-simplify: Simplify 0 into 0 1536750491.452 * [misc]backup-simplify: Simplify 0 into 0 1536750491.453 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750491.454 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536750491.455 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536750491.457 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.461 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750491.470 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536750491.471 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750491.471 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536750491.471 * [misc]backup-simplify: Simplify (- 0) into 0 1536750491.472 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.472 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750491.473 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1536750491.477 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750491.477 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1536750491.479 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1536750491.479 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.479 * [misc]backup-simplify: Simplify 0 into 0 1536750491.479 * [misc]backup-simplify: Simplify 0 into 0 1536750491.479 * [misc]backup-simplify: Simplify 0 into 0 1536750491.479 * [misc]backup-simplify: Simplify 0 into 0 1536750491.481 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750491.482 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536750491.482 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536750491.486 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 1536750491.486 * [misc]backup-simplify: Simplify (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1536750491.486 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1536750491.486 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1536750491.486 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750491.486 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1536750491.487 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1536750491.487 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750491.487 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750491.487 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.487 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.487 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750491.487 * [misc]taylor: Taking taylor expansion of k in k 1536750491.487 * [misc]backup-simplify: Simplify 0 into 0 1536750491.487 * [misc]backup-simplify: Simplify 1 into 1 1536750491.487 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750491.487 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.487 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.487 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1536750491.487 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536750491.487 * [misc]taylor: Taking taylor expansion of -2 in k 1536750491.487 * [misc]backup-simplify: Simplify -2 into -2 1536750491.487 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750491.487 * [misc]taylor: Taking taylor expansion of PI in k 1536750491.487 * [misc]backup-simplify: Simplify PI into PI 1536750491.487 * [misc]taylor: Taking taylor expansion of n in k 1536750491.487 * [misc]backup-simplify: Simplify n into n 1536750491.487 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750491.488 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536750491.488 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1536750491.488 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750491.488 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750491.488 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1536750491.489 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750491.489 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536750491.489 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536750491.489 * [misc]taylor: Taking taylor expansion of -1 in k 1536750491.489 * [misc]backup-simplify: Simplify -1 into -1 1536750491.489 * [misc]taylor: Taking taylor expansion of k in k 1536750491.489 * [misc]backup-simplify: Simplify 0 into 0 1536750491.489 * [misc]backup-simplify: Simplify 1 into 1 1536750491.489 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750491.489 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750491.490 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536750491.490 * [misc]backup-simplify: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750491.490 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1536750491.490 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750491.490 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536750491.490 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536750491.490 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750491.490 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750491.490 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.490 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.490 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750491.490 * [misc]taylor: Taking taylor expansion of k in n 1536750491.490 * [misc]backup-simplify: Simplify k into k 1536750491.491 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750491.491 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.491 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.491 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536750491.491 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536750491.491 * [misc]taylor: Taking taylor expansion of -2 in n 1536750491.491 * [misc]backup-simplify: Simplify -2 into -2 1536750491.491 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750491.491 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.491 * [misc]backup-simplify: Simplify PI into PI 1536750491.491 * [misc]taylor: Taking taylor expansion of n in n 1536750491.491 * [misc]backup-simplify: Simplify 0 into 0 1536750491.491 * [misc]backup-simplify: Simplify 1 into 1 1536750491.491 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750491.491 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536750491.492 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536750491.492 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750491.492 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750491.493 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750491.494 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1536750491.494 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536750491.494 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536750491.494 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536750491.495 * [misc]taylor: Taking taylor expansion of -1 in n 1536750491.495 * [misc]backup-simplify: Simplify -1 into -1 1536750491.495 * [misc]taylor: Taking taylor expansion of k in n 1536750491.495 * [misc]backup-simplify: Simplify k into k 1536750491.495 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536750491.495 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536750491.495 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536750491.495 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536750491.496 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 1536750491.496 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1536750491.496 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750491.496 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536750491.496 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536750491.496 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750491.496 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750491.496 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.496 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.496 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750491.496 * [misc]taylor: Taking taylor expansion of k in n 1536750491.496 * [misc]backup-simplify: Simplify k into k 1536750491.496 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750491.496 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750491.496 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.496 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536750491.496 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536750491.496 * [misc]taylor: Taking taylor expansion of -2 in n 1536750491.496 * [misc]backup-simplify: Simplify -2 into -2 1536750491.496 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750491.496 * [misc]taylor: Taking taylor expansion of PI in n 1536750491.496 * [misc]backup-simplify: Simplify PI into PI 1536750491.496 * [misc]taylor: Taking taylor expansion of n in n 1536750491.496 * [misc]backup-simplify: Simplify 0 into 0 1536750491.496 * [misc]backup-simplify: Simplify 1 into 1 1536750491.496 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750491.496 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536750491.497 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536750491.497 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750491.497 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750491.497 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750491.498 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1536750491.498 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536750491.498 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536750491.498 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536750491.498 * [misc]taylor: Taking taylor expansion of -1 in n 1536750491.498 * [misc]backup-simplify: Simplify -1 into -1 1536750491.498 * [misc]taylor: Taking taylor expansion of k in n 1536750491.498 * [misc]backup-simplify: Simplify k into k 1536750491.499 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536750491.499 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536750491.499 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536750491.499 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536750491.499 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 1536750491.499 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1536750491.499 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1536750491.499 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1536750491.499 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750491.499 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750491.499 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.499 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.499 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750491.499 * [misc]taylor: Taking taylor expansion of k in k 1536750491.499 * [misc]backup-simplify: Simplify 0 into 0 1536750491.499 * [misc]backup-simplify: Simplify 1 into 1 1536750491.500 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750491.500 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750491.500 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750491.500 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536750491.500 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536750491.500 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536750491.500 * [misc]taylor: Taking taylor expansion of -2 in k 1536750491.500 * [misc]backup-simplify: Simplify -2 into -2 1536750491.500 * [misc]taylor: Taking taylor expansion of PI in k 1536750491.500 * [misc]backup-simplify: Simplify PI into PI 1536750491.500 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536750491.500 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536750491.500 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750491.500 * [misc]taylor: Taking taylor expansion of n in k 1536750491.500 * [misc]backup-simplify: Simplify n into n 1536750491.500 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750491.501 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750491.501 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750491.501 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536750491.501 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536750491.501 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1536750491.502 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536750491.502 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536750491.502 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536750491.502 * [misc]taylor: Taking taylor expansion of -1 in k 1536750491.502 * [misc]backup-simplify: Simplify -1 into -1 1536750491.502 * [misc]taylor: Taking taylor expansion of k in k 1536750491.502 * [misc]backup-simplify: Simplify 0 into 0 1536750491.502 * [misc]backup-simplify: Simplify 1 into 1 1536750491.502 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750491.502 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750491.503 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536750491.503 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1536750491.504 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1536750491.504 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750491.505 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536750491.507 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1536750491.507 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750491.507 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750491.507 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.508 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750491.508 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1536750491.509 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750491.510 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1536750491.510 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.510 * [misc]backup-simplify: Simplify 0 into 0 1536750491.510 * [misc]backup-simplify: Simplify 0 into 0 1536750491.510 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536750491.511 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750491.511 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1536750491.512 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1536750491.513 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.514 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536750491.517 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1536750491.517 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750491.517 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750491.517 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750491.518 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750491.518 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1536750491.520 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750491.520 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750491.521 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1536750491.521 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1536750491.521 * [misc]taylor: Taking taylor expansion of 0 in k 1536750491.521 * [misc]backup-simplify: Simplify 0 into 0 1536750491.521 * [misc]backup-simplify: Simplify 0 into 0 1536750491.521 * [misc]backup-simplify: Simplify 0 into 0 1536750491.522 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750491.522 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750491.524 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1536750491.525 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1536750491.528 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 1536750491.528 * * * [misc]progress: simplifying candidates 1536750491.528 * * * * [misc]progress: [ 1 / 77 ] simplifiying candidate # 1536750491.528 * [enter]simplify: Simplifying (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) 1536750491.530 * * [misc]simplify: iters left: 6 (11 enodes) 1536750491.533 * * [misc]simplify: iters left: 5 (21 enodes) 1536750491.540 * * [misc]simplify: iters left: 4 (47 enodes) 1536750491.554 * * [misc]simplify: iters left: 3 (109 enodes) 1536750491.599 * * [misc]simplify: iters left: 2 (300 enodes) 1536750491.951 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) 1536750491.951 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI)))) (sqrt k))) 1536750491.951 * * * * [misc]progress: [ 2 / 77 ] simplifiying candidate # 1536750491.951 * * * * [misc]progress: [ 3 / 77 ] simplifiying candidate # 1536750491.951 * [enter]simplify: Simplifying (* PI (* n 2)) 1536750491.952 * * [misc]simplify: iters left: 4 (5 enodes) 1536750491.954 * * [misc]simplify: iters left: 3 (9 enodes) 1536750491.958 * * [misc]simplify: iters left: 2 (15 enodes) 1536750491.963 * * [misc]simplify: iters left: 1 (17 enodes) 1536750491.968 * [exit]simplify: Simplified to (* (* 2 n) PI) 1536750491.968 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* 2 n) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1536750491.968 * * * * [misc]progress: [ 4 / 77 ] simplifiying candidate # 1536750491.968 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (/ k 2)) 1536750491.968 * * [misc]simplify: iters left: 5 (8 enodes) 1536750491.970 * * [misc]simplify: iters left: 4 (12 enodes) 1536750491.973 * * [misc]simplify: iters left: 3 (18 enodes) 1536750491.975 * * [misc]simplify: iters left: 2 (20 enodes) 1536750491.978 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (/ k 2)) 1536750491.978 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) 1/2) (pow (* (* 2 n) PI) (/ k 2))) (sqrt k))) 1536750491.978 * * * * [misc]progress: [ 5 / 77 ] simplifiying candidate # 1536750491.979 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1536750491.979 * * [misc]simplify: iters left: 5 (6 enodes) 1536750491.980 * * [misc]simplify: iters left: 4 (8 enodes) 1536750491.981 * * [misc]simplify: iters left: 3 (11 enodes) 1536750491.983 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1536750491.983 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))) 1536750491.983 * * * * [misc]progress: [ 6 / 77 ] simplifiying candidate # 1536750491.983 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1536750491.984 * * [misc]simplify: iters left: 5 (6 enodes) 1536750491.985 * * [misc]simplify: iters left: 4 (8 enodes) 1536750491.986 * * [misc]simplify: iters left: 3 (11 enodes) 1536750491.988 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1536750491.988 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))) 1536750491.988 * * * * [misc]progress: [ 7 / 77 ] simplifiying candidate # 1536750491.988 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1536750491.988 * * [misc]simplify: iters left: 4 (5 enodes) 1536750491.989 * * [misc]simplify: iters left: 3 (7 enodes) 1536750491.990 * * [misc]simplify: iters left: 2 (10 enodes) 1536750491.992 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1536750491.992 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* PI (* n 2)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1536750491.992 * * * * [misc]progress: [ 8 / 77 ] simplifiying candidate # 1536750491.992 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1536750491.993 * * [misc]simplify: iters left: 5 (9 enodes) 1536750491.995 * * [misc]simplify: iters left: 4 (15 enodes) 1536750491.997 * * [misc]simplify: iters left: 3 (21 enodes) 1536750492.001 * * [misc]simplify: iters left: 2 (22 enodes) 1536750492.005 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1536750492.005 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1536750492.005 * * * * [misc]progress: [ 9 / 77 ] simplifiying candidate # 1536750492.006 * [enter]simplify: Simplifying (pow (* PI (* n 2)) (- (/ k 2))) 1536750492.006 * * [misc]simplify: iters left: 5 (9 enodes) 1536750492.009 * * [misc]simplify: iters left: 4 (15 enodes) 1536750492.014 * * [misc]simplify: iters left: 3 (21 enodes) 1536750492.020 * * [misc]simplify: iters left: 2 (22 enodes) 1536750492.027 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (- (/ k 2))) 1536750492.027 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* PI (* n 2)) 1/2) (pow (* (* PI n) 2) (- (/ k 2)))) (sqrt k))) 1536750492.027 * * * * [misc]progress: [ 10 / 77 ] simplifiying candidate # 1536750492.028 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1536750492.028 * * [misc]simplify: iters left: 5 (7 enodes) 1536750492.031 * * [misc]simplify: iters left: 4 (9 enodes) 1536750492.033 * * [misc]simplify: iters left: 3 (12 enodes) 1536750492.034 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1536750492.034 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (pow PI (- 1/2 (/ k 2))) (pow (* n 2) (- 1/2 (/ k 2)))) (sqrt k))) 1536750492.034 * * * * [misc]progress: [ 11 / 77 ] simplifiying candidate # 1536750492.034 * * * * [misc]progress: [ 12 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 13 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 14 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 15 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 16 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 17 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 18 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 19 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 20 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 21 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 22 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 23 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 24 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 25 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 26 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 27 / 77 ] simplifiying candidate # 1536750492.035 * * * * [misc]progress: [ 28 / 77 ] simplifiying candidate # 1536750492.035 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750492.036 * * [misc]simplify: iters left: 6 (14 enodes) 1536750492.040 * * [misc]simplify: iters left: 5 (26 enodes) 1536750492.046 * * [misc]simplify: iters left: 4 (53 enodes) 1536750492.064 * * [misc]simplify: iters left: 3 (137 enodes) 1536750492.163 * * [misc]simplify: iters left: 2 (487 enodes) 1536750493.087 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1536750493.087 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1536750493.087 * * * * [misc]progress: [ 29 / 77 ] simplifiying candidate # 1536750493.087 * [enter]simplify: Simplifying (- (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750493.089 * * [misc]simplify: iters left: 6 (14 enodes) 1536750493.095 * * [misc]simplify: iters left: 5 (26 enodes) 1536750493.108 * * [misc]simplify: iters left: 4 (53 enodes) 1536750493.134 * * [misc]simplify: iters left: 3 (137 enodes) 1536750493.221 * * [misc]simplify: iters left: 2 (487 enodes) 1536750494.120 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))) 1536750494.120 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* 2 n) PI))) (log (sqrt k))))) 1536750494.120 * * * * [misc]progress: [ 30 / 77 ] simplifiying candidate # 1536750494.120 * [enter]simplify: Simplifying (- (log (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1536750494.121 * * [misc]simplify: iters left: 6 (14 enodes) 1536750494.124 * * [misc]simplify: iters left: 5 (24 enodes) 1536750494.131 * * [misc]simplify: iters left: 4 (42 enodes) 1536750494.146 * * [misc]simplify: iters left: 3 (71 enodes) 1536750494.200 * * [misc]simplify: iters left: 2 (208 enodes) 1536750494.576 * [exit]simplify: Simplified to (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750494.576 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536750494.576 * * * * [misc]progress: [ 31 / 77 ] simplifiying candidate # 1536750494.577 * * * * [misc]progress: [ 32 / 77 ] simplifiying candidate # 1536750494.577 * * * * [misc]progress: [ 33 / 77 ] simplifiying candidate # 1536750494.577 * [enter]simplify: Simplifying (/ (* (* (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1536750494.579 * * [misc]simplify: iters left: 6 (16 enodes) 1536750494.587 * * [misc]simplify: iters left: 5 (31 enodes) 1536750494.603 * * [misc]simplify: iters left: 4 (67 enodes) 1536750494.638 * * [misc]simplify: iters left: 3 (124 enodes) 1536750494.671 * * [misc]simplify: iters left: 2 (195 enodes) 1536750494.757 * * [misc]simplify: iters left: 1 (309 enodes) 1536750494.945 * [exit]simplify: Simplified to (* (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (* k (sqrt k)))) 1536750494.946 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (* k (sqrt k)))))) 1536750494.946 * * * * [misc]progress: [ 34 / 77 ] simplifiying candidate # 1536750494.946 * * * * [misc]progress: [ 35 / 77 ] simplifiying candidate # 1536750494.946 * * * * [misc]progress: [ 36 / 77 ] simplifiying candidate # 1536750494.946 * * * * [misc]progress: [ 37 / 77 ] simplifiying candidate # 1536750494.946 * * * * [misc]progress: [ 38 / 77 ] simplifiying candidate # 1536750494.946 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750494.947 * * [misc]simplify: iters left: 6 (12 enodes) 1536750494.949 * * [misc]simplify: iters left: 5 (19 enodes) 1536750494.952 * * [misc]simplify: iters left: 4 (25 enodes) 1536750494.956 * * [misc]simplify: iters left: 3 (26 enodes) 1536750494.961 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750494.961 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))))) 1536750494.961 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1536750494.963 * * [misc]simplify: iters left: 6 (12 enodes) 1536750494.968 * * [misc]simplify: iters left: 5 (18 enodes) 1536750494.974 * * [misc]simplify: iters left: 4 (24 enodes) 1536750494.982 * * [misc]simplify: iters left: 3 (25 enodes) 1536750494.992 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1536750494.992 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))))) 1536750494.992 * * * * [misc]progress: [ 39 / 77 ] simplifiying candidate # 1536750494.992 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1536750494.993 * * [misc]simplify: iters left: 6 (11 enodes) 1536750494.998 * * [misc]simplify: iters left: 5 (16 enodes) 1536750495.003 * * [misc]simplify: iters left: 4 (22 enodes) 1536750495.010 * * [misc]simplify: iters left: 3 (24 enodes) 1536750495.018 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1536750495.018 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))))) 1536750495.018 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1536750495.020 * * [misc]simplify: iters left: 6 (12 enodes) 1536750495.025 * * [misc]simplify: iters left: 5 (18 enodes) 1536750495.031 * * [misc]simplify: iters left: 4 (24 enodes) 1536750495.035 * * [misc]simplify: iters left: 3 (25 enodes) 1536750495.039 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1536750495.039 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))))) 1536750495.039 * * * * [misc]progress: [ 40 / 77 ] simplifiying candidate # 1536750495.039 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1536750495.039 * * [misc]simplify: iters left: 6 (9 enodes) 1536750495.042 * * [misc]simplify: iters left: 5 (16 enodes) 1536750495.045 * * [misc]simplify: iters left: 4 (24 enodes) 1536750495.048 * * [misc]simplify: iters left: 3 (26 enodes) 1536750495.051 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1536750495.051 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536750495.052 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1536750495.052 * * [misc]simplify: iters left: 6 (11 enodes) 1536750495.054 * * [misc]simplify: iters left: 5 (17 enodes) 1536750495.057 * * [misc]simplify: iters left: 4 (23 enodes) 1536750495.061 * * [misc]simplify: iters left: 3 (24 enodes) 1536750495.065 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1536750495.065 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536750495.065 * * * * [misc]progress: [ 41 / 77 ] simplifiying candidate # 1536750495.065 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750495.066 * * [misc]simplify: iters left: 6 (12 enodes) 1536750495.068 * * [misc]simplify: iters left: 5 (19 enodes) 1536750495.072 * * [misc]simplify: iters left: 4 (25 enodes) 1536750495.080 * * [misc]simplify: iters left: 3 (26 enodes) 1536750495.090 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750495.090 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))))) 1536750495.090 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (cbrt (sqrt k))) 1536750495.092 * * [misc]simplify: iters left: 6 (12 enodes) 1536750495.096 * * [misc]simplify: iters left: 5 (18 enodes) 1536750495.103 * * [misc]simplify: iters left: 4 (24 enodes) 1536750495.110 * * [misc]simplify: iters left: 3 (25 enodes) 1536750495.118 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))) 1536750495.118 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 n) PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (cbrt (sqrt k))))) 1536750495.118 * * * * [misc]progress: [ 42 / 77 ] simplifiying candidate # 1536750495.118 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) (sqrt (sqrt k))) 1536750495.119 * * [misc]simplify: iters left: 6 (11 enodes) 1536750495.124 * * [misc]simplify: iters left: 5 (16 enodes) 1536750495.129 * * [misc]simplify: iters left: 4 (22 enodes) 1536750495.136 * * [misc]simplify: iters left: 3 (24 enodes) 1536750495.143 * [exit]simplify: Simplified to (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) 1536750495.143 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))))) 1536750495.144 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt (sqrt k))) 1536750495.145 * * [misc]simplify: iters left: 6 (12 enodes) 1536750495.149 * * [misc]simplify: iters left: 5 (18 enodes) 1536750495.156 * * [misc]simplify: iters left: 4 (24 enodes) 1536750495.163 * * [misc]simplify: iters left: 3 (25 enodes) 1536750495.171 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))) 1536750495.171 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt (sqrt k))))) 1536750495.171 * * * * [misc]progress: [ 43 / 77 ] simplifiying candidate # 1536750495.171 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) 1/2) 1) 1536750495.172 * * [misc]simplify: iters left: 6 (9 enodes) 1536750495.177 * * [misc]simplify: iters left: 5 (16 enodes) 1536750495.184 * * [misc]simplify: iters left: 4 (24 enodes) 1536750495.190 * * [misc]simplify: iters left: 3 (26 enodes) 1536750495.197 * [exit]simplify: Simplified to (sqrt (* (* PI 2) n)) 1536750495.197 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)))) 1536750495.197 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- (/ k 2))) (sqrt k)) 1536750495.198 * * [misc]simplify: iters left: 6 (11 enodes) 1536750495.203 * * [misc]simplify: iters left: 5 (17 enodes) 1536750495.210 * * [misc]simplify: iters left: 4 (23 enodes) 1536750495.217 * * [misc]simplify: iters left: 3 (24 enodes) 1536750495.225 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)) 1536750495.225 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* PI 2) n)) (/ (pow (* (* 2 n) PI) (- (/ k 2))) (sqrt k)))) 1536750495.225 * * * * [misc]progress: [ 44 / 77 ] simplifiying candidate # 1536750495.225 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750495.228 * * [misc]simplify: iters left: 6 (11 enodes) 1536750495.232 * * [misc]simplify: iters left: 5 (15 enodes) 1536750495.238 * * [misc]simplify: iters left: 4 (18 enodes) 1536750495.244 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750495.244 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536750495.244 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750495.245 * * [misc]simplify: iters left: 6 (11 enodes) 1536750495.249 * * [misc]simplify: iters left: 5 (14 enodes) 1536750495.254 * * [misc]simplify: iters left: 4 (17 enodes) 1536750495.259 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750495.259 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536750495.259 * * * * [misc]progress: [ 45 / 77 ] simplifiying candidate # 1536750495.260 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750495.261 * * [misc]simplify: iters left: 6 (10 enodes) 1536750495.264 * * [misc]simplify: iters left: 5 (12 enodes) 1536750495.268 * * [misc]simplify: iters left: 4 (15 enodes) 1536750495.274 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750495.274 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536750495.274 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750495.275 * * [misc]simplify: iters left: 6 (11 enodes) 1536750495.279 * * [misc]simplify: iters left: 5 (14 enodes) 1536750495.284 * * [misc]simplify: iters left: 4 (17 enodes) 1536750495.290 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750495.290 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536750495.290 * * * * [misc]progress: [ 46 / 77 ] simplifiying candidate # 1536750495.290 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) 1) 1536750495.291 * * [misc]simplify: iters left: 6 (9 enodes) 1536750495.294 * * [misc]simplify: iters left: 5 (13 enodes) 1536750495.299 * * [misc]simplify: iters left: 4 (18 enodes) 1536750495.304 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1536750495.304 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1536750495.304 * [enter]simplify: Simplifying (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1536750495.305 * * [misc]simplify: iters left: 6 (10 enodes) 1536750495.309 * * [misc]simplify: iters left: 5 (13 enodes) 1536750495.313 * * [misc]simplify: iters left: 4 (16 enodes) 1536750495.318 * [exit]simplify: Simplified to (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)) 1536750495.319 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow PI (- 1/2 (/ k 2))) (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt k)))) 1536750495.319 * * * * [misc]progress: [ 47 / 77 ] simplifiying candidate # 1536750495.319 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750495.320 * * [misc]simplify: iters left: 6 (16 enodes) 1536750495.328 * * [misc]simplify: iters left: 5 (28 enodes) 1536750495.340 * * [misc]simplify: iters left: 4 (46 enodes) 1536750495.355 * * [misc]simplify: iters left: 3 (50 enodes) 1536750495.368 * * [misc]simplify: iters left: 2 (53 enodes) 1536750495.391 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1536750495.391 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536750495.392 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750495.393 * * [misc]simplify: iters left: 6 (14 enodes) 1536750495.399 * * [misc]simplify: iters left: 5 (20 enodes) 1536750495.406 * * [misc]simplify: iters left: 4 (29 enodes) 1536750495.415 * * [misc]simplify: iters left: 3 (30 enodes) 1536750495.425 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750495.425 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536750495.425 * * * * [misc]progress: [ 48 / 77 ] simplifiying candidate # 1536750495.425 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1536750495.427 * * [misc]simplify: iters left: 6 (15 enodes) 1536750495.433 * * [misc]simplify: iters left: 5 (23 enodes) 1536750495.442 * * [misc]simplify: iters left: 4 (34 enodes) 1536750495.448 * * [misc]simplify: iters left: 3 (37 enodes) 1536750495.455 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) 1536750495.455 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536750495.455 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750495.456 * * [misc]simplify: iters left: 6 (14 enodes) 1536750495.458 * * [misc]simplify: iters left: 5 (20 enodes) 1536750495.462 * * [misc]simplify: iters left: 4 (29 enodes) 1536750495.466 * * [misc]simplify: iters left: 3 (30 enodes) 1536750495.471 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750495.471 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536750495.471 * * * * [misc]progress: [ 49 / 77 ] simplifiying candidate # 1536750495.471 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1) 1536750495.472 * * [misc]simplify: iters left: 6 (14 enodes) 1536750495.476 * * [misc]simplify: iters left: 5 (24 enodes) 1536750495.483 * * [misc]simplify: iters left: 4 (39 enodes) 1536750495.497 * * [misc]simplify: iters left: 3 (54 enodes) 1536750495.516 * * [misc]simplify: iters left: 2 (80 enodes) 1536750495.539 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) 1536750495.539 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)))) 1536750495.539 * [enter]simplify: Simplifying (/ (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1536750495.541 * * [misc]simplify: iters left: 6 (13 enodes) 1536750495.546 * * [misc]simplify: iters left: 5 (19 enodes) 1536750495.554 * * [misc]simplify: iters left: 4 (28 enodes) 1536750495.563 * * [misc]simplify: iters left: 3 (30 enodes) 1536750495.573 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536750495.573 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)))) 1536750495.573 * * * * [misc]progress: [ 50 / 77 ] simplifiying candidate # 1536750495.573 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750495.575 * * [misc]simplify: iters left: 6 (15 enodes) 1536750495.581 * * [misc]simplify: iters left: 5 (23 enodes) 1536750495.589 * * [misc]simplify: iters left: 4 (32 enodes) 1536750495.600 * * [misc]simplify: iters left: 3 (34 enodes) 1536750495.611 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750495.611 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536750495.611 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750495.615 * * [misc]simplify: iters left: 6 (14 enodes) 1536750495.621 * * [misc]simplify: iters left: 5 (20 enodes) 1536750495.629 * * [misc]simplify: iters left: 4 (29 enodes) 1536750495.638 * * [misc]simplify: iters left: 3 (30 enodes) 1536750495.648 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750495.648 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536750495.648 * * * * [misc]progress: [ 51 / 77 ] simplifiying candidate # 1536750495.648 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750495.650 * * [misc]simplify: iters left: 6 (14 enodes) 1536750495.655 * * [misc]simplify: iters left: 5 (20 enodes) 1536750495.663 * * [misc]simplify: iters left: 4 (29 enodes) 1536750495.671 * * [misc]simplify: iters left: 3 (30 enodes) 1536750495.680 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750495.680 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536750495.680 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750495.681 * * [misc]simplify: iters left: 6 (14 enodes) 1536750495.684 * * [misc]simplify: iters left: 5 (20 enodes) 1536750495.687 * * [misc]simplify: iters left: 4 (29 enodes) 1536750495.691 * * [misc]simplify: iters left: 3 (30 enodes) 1536750495.696 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750495.696 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536750495.696 * * * * [misc]progress: [ 52 / 77 ] simplifiying candidate # 1536750495.696 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1) 1536750495.697 * * [misc]simplify: iters left: 6 (13 enodes) 1536750495.700 * * [misc]simplify: iters left: 5 (21 enodes) 1536750495.705 * * [misc]simplify: iters left: 4 (32 enodes) 1536750495.713 * * [misc]simplify: iters left: 3 (33 enodes) 1536750495.723 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1536750495.723 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)))) 1536750495.723 * [enter]simplify: Simplifying (/ (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (sqrt k)) 1536750495.724 * * [misc]simplify: iters left: 6 (13 enodes) 1536750495.732 * * [misc]simplify: iters left: 5 (19 enodes) 1536750495.739 * * [misc]simplify: iters left: 4 (28 enodes) 1536750495.748 * * [misc]simplify: iters left: 3 (30 enodes) 1536750495.758 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536750495.758 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (sqrt k)))) 1536750495.758 * * * * [misc]progress: [ 53 / 77 ] simplifiying candidate # 1536750495.758 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750495.759 * * [misc]simplify: iters left: 6 (6 enodes) 1536750495.762 * * [misc]simplify: iters left: 5 (10 enodes) 1536750495.765 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1536750495.765 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536750495.766 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750495.767 * * [misc]simplify: iters left: 6 (13 enodes) 1536750495.769 * * [misc]simplify: iters left: 5 (19 enodes) 1536750495.773 * * [misc]simplify: iters left: 4 (28 enodes) 1536750495.777 * * [misc]simplify: iters left: 3 (30 enodes) 1536750495.782 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750495.782 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536750495.782 * * * * [misc]progress: [ 54 / 77 ] simplifiying candidate # 1536750495.782 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1536750495.782 * * [misc]simplify: iters left: 4 (5 enodes) 1536750495.783 * * [misc]simplify: iters left: 3 (7 enodes) 1536750495.784 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1536750495.784 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536750495.784 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750495.785 * * [misc]simplify: iters left: 6 (13 enodes) 1536750495.787 * * [misc]simplify: iters left: 5 (19 enodes) 1536750495.791 * * [misc]simplify: iters left: 4 (28 enodes) 1536750495.795 * * [misc]simplify: iters left: 3 (30 enodes) 1536750495.800 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750495.800 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536750495.800 * * * * [misc]progress: [ 55 / 77 ] simplifiying candidate # 1536750495.800 * [enter]simplify: Simplifying (/ 1 1) 1536750495.800 * * [misc]simplify: iters left: 2 (2 enodes) 1536750495.801 * * [misc]simplify: iters left: 1 (4 enodes) 1536750495.801 * [exit]simplify: Simplified to 1 1536750495.801 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))) 1536750495.801 * [enter]simplify: Simplifying (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 1536750495.802 * * [misc]simplify: iters left: 6 (12 enodes) 1536750495.805 * * [misc]simplify: iters left: 5 (18 enodes) 1536750495.808 * * [misc]simplify: iters left: 4 (27 enodes) 1536750495.812 * * [misc]simplify: iters left: 3 (29 enodes) 1536750495.817 * [exit]simplify: Simplified to (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)) 1536750495.817 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* 2 n) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536750495.817 * * * * [misc]progress: [ 56 / 77 ] simplifiying candidate # 1536750495.817 * * * * [misc]progress: [ 57 / 77 ] simplifiying candidate # 1536750495.817 * * * * [misc]progress: [ 58 / 77 ] simplifiying candidate # 1536750495.817 * * * * [misc]progress: [ 59 / 77 ] simplifiying candidate # 1536750495.817 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1536750495.819 * * [misc]simplify: iters left: 2 (3 enodes) 1536750495.819 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1536750495.819 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))) 1536750495.819 * * * * [misc]progress: [ 60 / 77 ] simplifiying candidate # 1536750495.819 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1536750495.820 * * [misc]simplify: iters left: 2 (3 enodes) 1536750495.820 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1536750495.820 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1536750495.820 * * * * [misc]progress: [ 61 / 77 ] simplifiying candidate # 1536750495.820 * [enter]simplify: Simplifying (sqrt k) 1536750495.820 * * [misc]simplify: iters left: 1 (2 enodes) 1536750495.821 * [exit]simplify: Simplified to (sqrt k) 1536750495.821 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1536750495.821 * * * * [misc]progress: [ 62 / 77 ] simplifiying candidate # 1536750495.821 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1536750495.821 * * [misc]simplify: iters left: 5 (7 enodes) 1536750495.823 * * [misc]simplify: iters left: 4 (12 enodes) 1536750495.825 * * [misc]simplify: iters left: 3 (18 enodes) 1536750495.828 * * [misc]simplify: iters left: 2 (20 enodes) 1536750495.831 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1536750495.831 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1536750495.831 * * * * [misc]progress: [ 63 / 77 ] simplifiying candidate # 1536750495.831 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1536750495.832 * * [misc]simplify: iters left: 5 (7 enodes) 1536750495.833 * * [misc]simplify: iters left: 4 (12 enodes) 1536750495.836 * * [misc]simplify: iters left: 3 (18 enodes) 1536750495.838 * * [misc]simplify: iters left: 2 (20 enodes) 1536750495.841 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1536750495.841 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (/ (sqrt k) (pow (* PI (* n 2)) (- (/ k 2)))))) 1536750495.841 * * * * [misc]progress: [ 64 / 77 ] simplifiying candidate # 1536750495.842 * [enter]simplify: Simplifying (pow PI (- 1/2 (/ k 2))) 1536750495.842 * * [misc]simplify: iters left: 5 (7 enodes) 1536750495.843 * * [misc]simplify: iters left: 4 (9 enodes) 1536750495.845 * * [misc]simplify: iters left: 3 (12 enodes) 1536750495.847 * [exit]simplify: Simplified to (pow PI (- 1/2 (/ k 2))) 1536750495.847 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n 2) (- 1/2 (/ k 2)))))) 1536750495.847 * * * * [misc]progress: [ 65 / 77 ] simplifiying candidate # 1536750495.847 * [enter]simplify: Simplifying (* (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) 1536750495.848 * * [misc]simplify: iters left: 6 (12 enodes) 1536750495.853 * * [misc]simplify: iters left: 5 (18 enodes) 1536750495.860 * * [misc]simplify: iters left: 4 (27 enodes) 1536750495.868 * * [misc]simplify: iters left: 3 (29 enodes) 1536750495.878 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) 1536750495.878 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1536750495.878 * * * * [misc]progress: [ 66 / 77 ] simplifiying candidate # 1536750495.878 * [enter]simplify: Simplifying (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) 1536750495.879 * * [misc]simplify: iters left: 6 (11 enodes) 1536750495.883 * * [misc]simplify: iters left: 5 (17 enodes) 1536750495.890 * * [misc]simplify: iters left: 4 (26 enodes) 1536750495.898 * * [misc]simplify: iters left: 3 (27 enodes) 1536750495.906 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1536750495.906 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* PI (* n 2)) (- 1/2 (/ k 2))))))) 1536750495.906 * * * * [misc]progress: [ 67 / 77 ] simplifiying candidate # 1536750495.906 * * * * [misc]progress: [ 68 / 77 ] simplifiying candidate # 1536750495.906 * [enter]simplify: Simplifying (pow (* PI (* n 2)) 1/2) 1536750495.907 * * [misc]simplify: iters left: 5 (7 enodes) 1536750495.911 * * [misc]simplify: iters left: 4 (12 enodes) 1536750495.915 * * [misc]simplify: iters left: 3 (18 enodes) 1536750495.921 * * [misc]simplify: iters left: 2 (20 enodes) 1536750495.927 * [exit]simplify: Simplified to (sqrt (* (* 2 n) PI)) 1536750495.927 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* 2 n) PI)) (* (sqrt k) (pow (* PI (* n 2)) (/ k 2))))) 1536750495.927 * * * * [misc]progress: [ 69 / 77 ] simplifiying candidate # 1536750495.927 * [enter]simplify: Simplifying (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1536750495.933 * * [misc]simplify: iters left: 6 (37 enodes) 1536750495.957 * * [misc]simplify: iters left: 5 (105 enodes) 1536750496.000 * * [misc]simplify: iters left: 4 (339 enodes) 1536750496.419 * [exit]simplify: Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) 1536750496.419 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt k))) 1536750496.419 * * * * [misc]progress: [ 70 / 77 ] simplifiying candidate # 1536750496.419 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1536750496.420 * * [misc]simplify: iters left: 6 (15 enodes) 1536750496.426 * * [misc]simplify: iters left: 5 (33 enodes) 1536750496.442 * * [misc]simplify: iters left: 4 (64 enodes) 1536750496.482 * * [misc]simplify: iters left: 3 (171 enodes) 1536750496.680 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1536750496.680 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k))) 1536750496.680 * * * * [misc]progress: [ 71 / 77 ] simplifiying candidate # 1536750496.680 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1536750496.681 * * [misc]simplify: iters left: 6 (15 enodes) 1536750496.694 * * [misc]simplify: iters left: 5 (30 enodes) 1536750496.710 * * [misc]simplify: iters left: 4 (65 enodes) 1536750496.751 * * [misc]simplify: iters left: 3 (200 enodes) 1536750496.981 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1536750496.981 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1536750496.981 * * * * [misc]progress: [ 72 / 77 ] simplifiying candidate # 1536750496.981 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536750496.982 * * [misc]simplify: iters left: 4 (5 enodes) 1536750496.983 * * [misc]simplify: iters left: 3 (9 enodes) 1536750496.985 * * [misc]simplify: iters left: 2 (15 enodes) 1536750496.987 * * [misc]simplify: iters left: 1 (17 enodes) 1536750496.990 * [exit]simplify: Simplified to (* (* PI n) 2) 1536750496.990 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1536750496.990 * * * * [misc]progress: [ 73 / 77 ] simplifiying candidate # 1536750496.990 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536750496.990 * * [misc]simplify: iters left: 4 (5 enodes) 1536750496.991 * * [misc]simplify: iters left: 3 (9 enodes) 1536750496.993 * * [misc]simplify: iters left: 2 (15 enodes) 1536750496.996 * * [misc]simplify: iters left: 1 (17 enodes) 1536750496.998 * [exit]simplify: Simplified to (* (* PI n) 2) 1536750496.998 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1536750496.998 * * * * [misc]progress: [ 74 / 77 ] simplifiying candidate # 1536750496.998 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536750496.999 * * [misc]simplify: iters left: 4 (5 enodes) 1536750497.000 * * [misc]simplify: iters left: 3 (9 enodes) 1536750497.002 * * [misc]simplify: iters left: 2 (15 enodes) 1536750497.005 * * [misc]simplify: iters left: 1 (17 enodes) 1536750497.007 * [exit]simplify: Simplified to (* (* PI n) 2) 1536750497.007 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k))) 1536750497.007 * * * * [misc]progress: [ 75 / 77 ] simplifiying candidate # 1536750497.007 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 1536750497.007 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536750497.007 * * * * [misc]progress: [ 76 / 77 ] simplifiying candidate # 1536750497.008 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 1536750497.008 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536750497.008 * * * * [misc]progress: [ 77 / 77 ] simplifiying candidate # 1536750497.008 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 1536750497.008 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536750497.008 * * * [misc]progress: adding candidates to table 1536750498.498 * * [misc]progress: iteration 2 / 4 1536750498.498 * * * [misc]progress: picking best candidate 1536750498.599 * * * * [misc]pick: Picked # 1536750498.599 * * * [misc]progress: localizing error 1536750498.622 * * * [misc]progress: generating rewritten candidates 1536750498.622 * * * * [misc]progress: [ 1 / 3 ] rewriting at (2 1) 1536750498.644 * * * * [misc]progress: [ 2 / 3 ] rewriting at (2 1 1 2) 1536750498.646 * * * * [misc]progress: [ 3 / 3 ] rewriting at (2) 1536750498.713 * * * [misc]progress: generating series expansions 1536750498.713 * * * * [misc]progress: [ 1 / 3 ] generating series at (2 1) 1536750498.713 * [misc]backup-simplify: Simplify (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 1536750498.713 * [misc]approximate: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 1536750498.713 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1536750498.714 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1536750498.714 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1536750498.714 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750498.714 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.714 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.714 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750498.714 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.714 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.714 * [misc]taylor: Taking taylor expansion of k in k 1536750498.714 * [misc]backup-simplify: Simplify 0 into 0 1536750498.714 * [misc]backup-simplify: Simplify 1 into 1 1536750498.714 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1536750498.714 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1536750498.714 * [misc]taylor: Taking taylor expansion of 2 in k 1536750498.714 * [misc]backup-simplify: Simplify 2 into 2 1536750498.714 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536750498.714 * [misc]taylor: Taking taylor expansion of n in k 1536750498.714 * [misc]backup-simplify: Simplify n into n 1536750498.714 * [misc]taylor: Taking taylor expansion of PI in k 1536750498.714 * [misc]backup-simplify: Simplify PI into PI 1536750498.714 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536750498.714 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1536750498.714 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1536750498.715 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750498.715 * [misc]backup-simplify: Simplify (- 0) into 0 1536750498.715 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750498.715 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1536750498.716 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1536750498.716 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536750498.716 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536750498.716 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536750498.716 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750498.716 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.716 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.716 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750498.716 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.716 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.716 * [misc]taylor: Taking taylor expansion of k in n 1536750498.716 * [misc]backup-simplify: Simplify k into k 1536750498.716 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536750498.716 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536750498.716 * [misc]taylor: Taking taylor expansion of 2 in n 1536750498.716 * [misc]backup-simplify: Simplify 2 into 2 1536750498.716 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750498.716 * [misc]taylor: Taking taylor expansion of n in n 1536750498.716 * [misc]backup-simplify: Simplify 0 into 0 1536750498.716 * [misc]backup-simplify: Simplify 1 into 1 1536750498.716 * [misc]taylor: Taking taylor expansion of PI in n 1536750498.716 * [misc]backup-simplify: Simplify PI into PI 1536750498.717 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750498.717 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536750498.717 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750498.718 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536750498.719 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750498.719 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750498.719 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750498.719 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750498.720 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750498.720 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1536750498.721 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1536750498.721 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536750498.721 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536750498.721 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536750498.721 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750498.721 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.721 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.721 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750498.721 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.721 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.721 * [misc]taylor: Taking taylor expansion of k in n 1536750498.722 * [misc]backup-simplify: Simplify k into k 1536750498.722 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536750498.722 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536750498.722 * [misc]taylor: Taking taylor expansion of 2 in n 1536750498.722 * [misc]backup-simplify: Simplify 2 into 2 1536750498.722 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750498.722 * [misc]taylor: Taking taylor expansion of n in n 1536750498.722 * [misc]backup-simplify: Simplify 0 into 0 1536750498.722 * [misc]backup-simplify: Simplify 1 into 1 1536750498.722 * [misc]taylor: Taking taylor expansion of PI in n 1536750498.722 * [misc]backup-simplify: Simplify PI into PI 1536750498.722 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750498.722 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536750498.723 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750498.724 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536750498.724 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750498.724 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750498.724 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750498.725 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750498.725 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750498.726 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1536750498.727 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1536750498.727 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1536750498.727 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1536750498.727 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750498.727 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.727 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.727 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750498.727 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.727 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.727 * [misc]taylor: Taking taylor expansion of k in k 1536750498.727 * [misc]backup-simplify: Simplify 0 into 0 1536750498.727 * [misc]backup-simplify: Simplify 1 into 1 1536750498.727 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536750498.727 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750498.727 * [misc]taylor: Taking taylor expansion of n in k 1536750498.727 * [misc]backup-simplify: Simplify n into n 1536750498.727 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750498.727 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536750498.727 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536750498.727 * [misc]taylor: Taking taylor expansion of 2 in k 1536750498.727 * [misc]backup-simplify: Simplify 2 into 2 1536750498.727 * [misc]taylor: Taking taylor expansion of PI in k 1536750498.728 * [misc]backup-simplify: Simplify PI into PI 1536750498.728 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750498.728 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750498.729 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750498.729 * [misc]backup-simplify: Simplify (- 0) into 0 1536750498.729 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750498.730 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750498.730 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1536750498.731 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1536750498.732 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1536750498.733 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536750498.735 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536750498.738 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536750498.738 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536750498.738 * [misc]backup-simplify: Simplify (- 0) into 0 1536750498.738 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750498.739 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750498.740 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1536750498.742 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750498.742 * [misc]taylor: Taking taylor expansion of 0 in k 1536750498.742 * [misc]backup-simplify: Simplify 0 into 0 1536750498.742 * [misc]backup-simplify: Simplify 0 into 0 1536750498.743 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536750498.743 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536750498.747 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536750498.747 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750498.747 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536750498.747 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750498.747 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750498.748 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1536750498.750 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536750498.752 * [misc]backup-simplify: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536750498.753 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750498.755 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536750498.761 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536750498.762 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536750498.762 * [misc]backup-simplify: Simplify (- 0) into 0 1536750498.762 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750498.763 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750498.764 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536750498.766 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750498.766 * [misc]taylor: Taking taylor expansion of 0 in k 1536750498.766 * [misc]backup-simplify: Simplify 0 into 0 1536750498.766 * [misc]backup-simplify: Simplify 0 into 0 1536750498.766 * [misc]backup-simplify: Simplify 0 into 0 1536750498.769 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536750498.770 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536750498.776 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536750498.776 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750498.776 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536750498.777 * [misc]backup-simplify: Simplify (- 0) into 0 1536750498.777 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750498.778 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536750498.781 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1536750498.785 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1536750498.791 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1536750498.791 * [misc]backup-simplify: Simplify (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536750498.791 * [misc]approximate: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1536750498.791 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750498.791 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1536750498.791 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1536750498.791 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750498.791 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.792 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.792 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750498.792 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.792 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.792 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750498.792 * [misc]taylor: Taking taylor expansion of k in k 1536750498.792 * [misc]backup-simplify: Simplify 0 into 0 1536750498.792 * [misc]backup-simplify: Simplify 1 into 1 1536750498.792 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750498.792 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1536750498.792 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1536750498.792 * [misc]taylor: Taking taylor expansion of 2 in k 1536750498.792 * [misc]backup-simplify: Simplify 2 into 2 1536750498.792 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750498.792 * [misc]taylor: Taking taylor expansion of PI in k 1536750498.792 * [misc]backup-simplify: Simplify PI into PI 1536750498.792 * [misc]taylor: Taking taylor expansion of n in k 1536750498.792 * [misc]backup-simplify: Simplify n into n 1536750498.792 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750498.792 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1536750498.792 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1536750498.792 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750498.792 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750498.792 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750498.793 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1536750498.793 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536750498.793 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750498.793 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536750498.793 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536750498.793 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750498.793 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.793 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.793 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750498.793 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.793 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.793 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750498.793 * [misc]taylor: Taking taylor expansion of k in n 1536750498.793 * [misc]backup-simplify: Simplify k into k 1536750498.793 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750498.793 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536750498.793 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536750498.793 * [misc]taylor: Taking taylor expansion of 2 in n 1536750498.793 * [misc]backup-simplify: Simplify 2 into 2 1536750498.793 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750498.793 * [misc]taylor: Taking taylor expansion of PI in n 1536750498.793 * [misc]backup-simplify: Simplify PI into PI 1536750498.793 * [misc]taylor: Taking taylor expansion of n in n 1536750498.793 * [misc]backup-simplify: Simplify 0 into 0 1536750498.793 * [misc]backup-simplify: Simplify 1 into 1 1536750498.793 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750498.794 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750498.794 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750498.794 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750498.794 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750498.794 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750498.795 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750498.795 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1536750498.795 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536750498.796 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750498.796 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536750498.796 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536750498.796 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750498.796 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.796 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.796 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750498.796 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.796 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.796 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750498.796 * [misc]taylor: Taking taylor expansion of k in n 1536750498.796 * [misc]backup-simplify: Simplify k into k 1536750498.796 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750498.796 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536750498.796 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536750498.796 * [misc]taylor: Taking taylor expansion of 2 in n 1536750498.796 * [misc]backup-simplify: Simplify 2 into 2 1536750498.796 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750498.796 * [misc]taylor: Taking taylor expansion of PI in n 1536750498.796 * [misc]backup-simplify: Simplify PI into PI 1536750498.796 * [misc]taylor: Taking taylor expansion of n in n 1536750498.796 * [misc]backup-simplify: Simplify 0 into 0 1536750498.796 * [misc]backup-simplify: Simplify 1 into 1 1536750498.796 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750498.796 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750498.797 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750498.797 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750498.797 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750498.797 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750498.797 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750498.798 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1536750498.798 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536750498.799 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1536750498.799 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1536750498.799 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750498.799 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.799 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.799 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750498.799 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.799 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.799 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750498.799 * [misc]taylor: Taking taylor expansion of k in k 1536750498.799 * [misc]backup-simplify: Simplify 0 into 0 1536750498.799 * [misc]backup-simplify: Simplify 1 into 1 1536750498.799 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750498.799 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536750498.799 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536750498.799 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536750498.799 * [misc]taylor: Taking taylor expansion of 2 in k 1536750498.799 * [misc]backup-simplify: Simplify 2 into 2 1536750498.799 * [misc]taylor: Taking taylor expansion of PI in k 1536750498.799 * [misc]backup-simplify: Simplify PI into PI 1536750498.799 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750498.800 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750498.800 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750498.800 * [misc]taylor: Taking taylor expansion of n in k 1536750498.800 * [misc]backup-simplify: Simplify n into n 1536750498.800 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750498.800 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750498.800 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750498.800 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750498.800 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536750498.800 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536750498.801 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536750498.801 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536750498.802 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536750498.802 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750498.803 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536750498.808 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536750498.808 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750498.808 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750498.808 * [misc]backup-simplify: Simplify (- 0) into 0 1536750498.809 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750498.809 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750498.810 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1536750498.811 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750498.811 * [misc]taylor: Taking taylor expansion of 0 in k 1536750498.811 * [misc]backup-simplify: Simplify 0 into 0 1536750498.811 * [misc]backup-simplify: Simplify 0 into 0 1536750498.811 * [misc]backup-simplify: Simplify 0 into 0 1536750498.812 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750498.812 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536750498.816 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536750498.816 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750498.817 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750498.817 * [misc]backup-simplify: Simplify (- 0) into 0 1536750498.817 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750498.817 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750498.818 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1536750498.819 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750498.819 * [misc]taylor: Taking taylor expansion of 0 in k 1536750498.819 * [misc]backup-simplify: Simplify 0 into 0 1536750498.819 * [misc]backup-simplify: Simplify 0 into 0 1536750498.819 * [misc]backup-simplify: Simplify 0 into 0 1536750498.819 * [misc]backup-simplify: Simplify 0 into 0 1536750498.821 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750498.822 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750498.830 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536750498.830 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750498.831 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536750498.831 * [misc]backup-simplify: Simplify (- 0) into 0 1536750498.831 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750498.832 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750498.833 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1536750498.837 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750498.837 * [misc]taylor: Taking taylor expansion of 0 in k 1536750498.837 * [misc]backup-simplify: Simplify 0 into 0 1536750498.837 * [misc]backup-simplify: Simplify 0 into 0 1536750498.838 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1536750498.838 * [misc]backup-simplify: Simplify (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750498.838 * [misc]approximate: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1536750498.838 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750498.838 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1536750498.838 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1536750498.838 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750498.838 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750498.838 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.838 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.838 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750498.839 * [misc]taylor: Taking taylor expansion of k in k 1536750498.839 * [misc]backup-simplify: Simplify 0 into 0 1536750498.839 * [misc]backup-simplify: Simplify 1 into 1 1536750498.839 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750498.839 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.839 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.839 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1536750498.839 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536750498.839 * [misc]taylor: Taking taylor expansion of -2 in k 1536750498.839 * [misc]backup-simplify: Simplify -2 into -2 1536750498.839 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750498.839 * [misc]taylor: Taking taylor expansion of PI in k 1536750498.839 * [misc]backup-simplify: Simplify PI into PI 1536750498.839 * [misc]taylor: Taking taylor expansion of n in k 1536750498.839 * [misc]backup-simplify: Simplify n into n 1536750498.839 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750498.839 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536750498.840 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1536750498.840 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750498.840 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750498.840 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1536750498.840 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750498.840 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750498.840 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536750498.840 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536750498.841 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750498.841 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750498.841 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.841 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.841 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750498.841 * [misc]taylor: Taking taylor expansion of k in n 1536750498.841 * [misc]backup-simplify: Simplify k into k 1536750498.841 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750498.841 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.841 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.841 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536750498.841 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536750498.841 * [misc]taylor: Taking taylor expansion of -2 in n 1536750498.841 * [misc]backup-simplify: Simplify -2 into -2 1536750498.841 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750498.841 * [misc]taylor: Taking taylor expansion of PI in n 1536750498.841 * [misc]backup-simplify: Simplify PI into PI 1536750498.841 * [misc]taylor: Taking taylor expansion of n in n 1536750498.841 * [misc]backup-simplify: Simplify 0 into 0 1536750498.841 * [misc]backup-simplify: Simplify 1 into 1 1536750498.841 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750498.842 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536750498.842 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536750498.842 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750498.842 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750498.843 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750498.844 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1536750498.845 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536750498.845 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750498.845 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536750498.845 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536750498.845 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750498.845 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750498.845 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.845 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.845 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750498.845 * [misc]taylor: Taking taylor expansion of k in n 1536750498.845 * [misc]backup-simplify: Simplify k into k 1536750498.845 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750498.845 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.845 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.845 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536750498.845 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536750498.845 * [misc]taylor: Taking taylor expansion of -2 in n 1536750498.845 * [misc]backup-simplify: Simplify -2 into -2 1536750498.845 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750498.845 * [misc]taylor: Taking taylor expansion of PI in n 1536750498.846 * [misc]backup-simplify: Simplify PI into PI 1536750498.846 * [misc]taylor: Taking taylor expansion of n in n 1536750498.846 * [misc]backup-simplify: Simplify 0 into 0 1536750498.846 * [misc]backup-simplify: Simplify 1 into 1 1536750498.846 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750498.846 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536750498.847 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536750498.847 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750498.847 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750498.848 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750498.848 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1536750498.849 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536750498.849 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1536750498.849 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1536750498.849 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750498.849 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750498.849 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.849 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.849 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750498.849 * [misc]taylor: Taking taylor expansion of k in k 1536750498.850 * [misc]backup-simplify: Simplify 0 into 0 1536750498.850 * [misc]backup-simplify: Simplify 1 into 1 1536750498.850 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750498.850 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.850 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.850 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536750498.850 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536750498.850 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536750498.850 * [misc]taylor: Taking taylor expansion of -2 in k 1536750498.850 * [misc]backup-simplify: Simplify -2 into -2 1536750498.850 * [misc]taylor: Taking taylor expansion of PI in k 1536750498.850 * [misc]backup-simplify: Simplify PI into PI 1536750498.850 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536750498.851 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536750498.851 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750498.851 * [misc]taylor: Taking taylor expansion of n in k 1536750498.851 * [misc]backup-simplify: Simplify n into n 1536750498.851 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750498.851 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750498.851 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750498.851 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536750498.852 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536750498.853 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1536750498.853 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536750498.854 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536750498.855 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750498.856 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536750498.859 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1536750498.859 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750498.860 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750498.860 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750498.861 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750498.862 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1536750498.864 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750498.864 * [misc]taylor: Taking taylor expansion of 0 in k 1536750498.864 * [misc]backup-simplify: Simplify 0 into 0 1536750498.864 * [misc]backup-simplify: Simplify 0 into 0 1536750498.864 * [misc]backup-simplify: Simplify 0 into 0 1536750498.865 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750498.867 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536750498.873 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1536750498.873 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750498.873 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750498.873 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750498.874 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750498.875 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1536750498.878 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750498.878 * [misc]taylor: Taking taylor expansion of 0 in k 1536750498.878 * [misc]backup-simplify: Simplify 0 into 0 1536750498.878 * [misc]backup-simplify: Simplify 0 into 0 1536750498.878 * [misc]backup-simplify: Simplify 0 into 0 1536750498.878 * [misc]backup-simplify: Simplify 0 into 0 1536750498.880 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750498.881 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750498.890 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 1536750498.891 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750498.891 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536750498.891 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750498.892 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750498.893 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 1536750498.897 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750498.897 * [misc]taylor: Taking taylor expansion of 0 in k 1536750498.897 * [misc]backup-simplify: Simplify 0 into 0 1536750498.897 * [misc]backup-simplify: Simplify 0 into 0 1536750498.899 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1536750498.899 * * * * [misc]progress: [ 2 / 3 ] generating series at (2 1 1 2) 1536750498.899 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536750498.899 * [misc]approximate: Taking taylor expansion of (* n PI) in (n) around 0 1536750498.899 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750498.899 * [misc]taylor: Taking taylor expansion of n in n 1536750498.899 * [misc]backup-simplify: Simplify 0 into 0 1536750498.899 * [misc]backup-simplify: Simplify 1 into 1 1536750498.899 * [misc]taylor: Taking taylor expansion of PI in n 1536750498.899 * [misc]backup-simplify: Simplify PI into PI 1536750498.899 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750498.899 * [misc]taylor: Taking taylor expansion of n in n 1536750498.899 * [misc]backup-simplify: Simplify 0 into 0 1536750498.899 * [misc]backup-simplify: Simplify 1 into 1 1536750498.900 * [misc]taylor: Taking taylor expansion of PI in n 1536750498.900 * [misc]backup-simplify: Simplify PI into PI 1536750498.900 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750498.900 * [misc]backup-simplify: Simplify 0 into 0 1536750498.901 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750498.901 * [misc]backup-simplify: Simplify PI into PI 1536750498.902 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536750498.902 * [misc]backup-simplify: Simplify 0 into 0 1536750498.904 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750498.904 * [misc]backup-simplify: Simplify 0 into 0 1536750498.906 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536750498.906 * [misc]backup-simplify: Simplify 0 into 0 1536750498.909 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536750498.909 * [misc]backup-simplify: Simplify 0 into 0 1536750498.912 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536750498.913 * [misc]backup-simplify: Simplify 0 into 0 1536750498.917 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1536750498.917 * [misc]backup-simplify: Simplify 0 into 0 1536750498.917 * [misc]backup-simplify: Simplify (* PI n) into (* n PI) 1536750498.917 * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) 1536750498.918 * [misc]approximate: Taking taylor expansion of (/ PI n) in (n) around 0 1536750498.918 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750498.918 * [misc]taylor: Taking taylor expansion of PI in n 1536750498.918 * [misc]backup-simplify: Simplify PI into PI 1536750498.918 * [misc]taylor: Taking taylor expansion of n in n 1536750498.918 * [misc]backup-simplify: Simplify 0 into 0 1536750498.918 * [misc]backup-simplify: Simplify 1 into 1 1536750498.918 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750498.918 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750498.918 * [misc]taylor: Taking taylor expansion of PI in n 1536750498.918 * [misc]backup-simplify: Simplify PI into PI 1536750498.918 * [misc]taylor: Taking taylor expansion of n in n 1536750498.918 * [misc]backup-simplify: Simplify 0 into 0 1536750498.918 * [misc]backup-simplify: Simplify 1 into 1 1536750498.919 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750498.919 * [misc]backup-simplify: Simplify PI into PI 1536750498.920 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750498.920 * [misc]backup-simplify: Simplify 0 into 0 1536750498.921 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750498.921 * [misc]backup-simplify: Simplify 0 into 0 1536750498.923 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750498.923 * [misc]backup-simplify: Simplify 0 into 0 1536750498.925 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750498.925 * [misc]backup-simplify: Simplify 0 into 0 1536750498.927 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750498.927 * [misc]backup-simplify: Simplify 0 into 0 1536750498.930 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750498.930 * [misc]backup-simplify: Simplify 0 into 0 1536750498.930 * [misc]backup-simplify: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 1536750498.930 * [misc]backup-simplify: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 1536750498.930 * [misc]approximate: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 1536750498.931 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536750498.931 * [misc]taylor: Taking taylor expansion of -1 in n 1536750498.931 * [misc]backup-simplify: Simplify -1 into -1 1536750498.931 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750498.931 * [misc]taylor: Taking taylor expansion of PI in n 1536750498.931 * [misc]backup-simplify: Simplify PI into PI 1536750498.931 * [misc]taylor: Taking taylor expansion of n in n 1536750498.931 * [misc]backup-simplify: Simplify 0 into 0 1536750498.931 * [misc]backup-simplify: Simplify 1 into 1 1536750498.931 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750498.931 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536750498.931 * [misc]taylor: Taking taylor expansion of -1 in n 1536750498.931 * [misc]backup-simplify: Simplify -1 into -1 1536750498.931 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750498.931 * [misc]taylor: Taking taylor expansion of PI in n 1536750498.931 * [misc]backup-simplify: Simplify PI into PI 1536750498.931 * [misc]taylor: Taking taylor expansion of n in n 1536750498.931 * [misc]backup-simplify: Simplify 0 into 0 1536750498.931 * [misc]backup-simplify: Simplify 1 into 1 1536750498.932 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750498.932 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536750498.932 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536750498.934 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750498.934 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 PI)) into 0 1536750498.934 * [misc]backup-simplify: Simplify 0 into 0 1536750498.936 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750498.937 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 1536750498.937 * [misc]backup-simplify: Simplify 0 into 0 1536750498.939 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750498.941 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750498.941 * [misc]backup-simplify: Simplify 0 into 0 1536750498.943 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750498.945 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536750498.945 * [misc]backup-simplify: Simplify 0 into 0 1536750498.947 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750498.950 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536750498.950 * [misc]backup-simplify: Simplify 0 into 0 1536750498.953 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750498.959 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536750498.959 * [misc]backup-simplify: Simplify 0 into 0 1536750498.959 * [misc]backup-simplify: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 1536750498.959 * * * * [misc]progress: [ 3 / 3 ] generating series at (2) 1536750498.960 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 1536750498.960 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 1536750498.960 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 1536750498.960 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536750498.960 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750498.960 * [misc]taylor: Taking taylor expansion of k in k 1536750498.960 * [misc]backup-simplify: Simplify 0 into 0 1536750498.961 * [misc]backup-simplify: Simplify 1 into 1 1536750498.961 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750498.961 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750498.961 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750498.961 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 1536750498.961 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 1536750498.961 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 1536750498.962 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750498.962 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.962 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.962 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750498.962 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.962 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.962 * [misc]taylor: Taking taylor expansion of k in k 1536750498.962 * [misc]backup-simplify: Simplify 0 into 0 1536750498.962 * [misc]backup-simplify: Simplify 1 into 1 1536750498.962 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in k 1536750498.962 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in k 1536750498.962 * [misc]taylor: Taking taylor expansion of 2 in k 1536750498.962 * [misc]backup-simplify: Simplify 2 into 2 1536750498.962 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536750498.962 * [misc]taylor: Taking taylor expansion of n in k 1536750498.962 * [misc]backup-simplify: Simplify n into n 1536750498.962 * [misc]taylor: Taking taylor expansion of PI in k 1536750498.962 * [misc]backup-simplify: Simplify PI into PI 1536750498.962 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536750498.962 * [misc]backup-simplify: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 1536750498.962 * [misc]backup-simplify: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 1536750498.963 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750498.963 * [misc]backup-simplify: Simplify (- 0) into 0 1536750498.963 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750498.963 * [misc]backup-simplify: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 1536750498.963 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 1536750498.964 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1536750498.964 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536750498.964 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750498.964 * [misc]taylor: Taking taylor expansion of k in n 1536750498.964 * [misc]backup-simplify: Simplify k into k 1536750498.964 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750498.964 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536750498.964 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750498.964 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536750498.964 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536750498.964 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536750498.964 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536750498.964 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750498.964 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.964 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.964 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750498.964 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.964 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.965 * [misc]taylor: Taking taylor expansion of k in n 1536750498.965 * [misc]backup-simplify: Simplify k into k 1536750498.965 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536750498.965 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536750498.965 * [misc]taylor: Taking taylor expansion of 2 in n 1536750498.965 * [misc]backup-simplify: Simplify 2 into 2 1536750498.965 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750498.965 * [misc]taylor: Taking taylor expansion of n in n 1536750498.965 * [misc]backup-simplify: Simplify 0 into 0 1536750498.965 * [misc]backup-simplify: Simplify 1 into 1 1536750498.965 * [misc]taylor: Taking taylor expansion of PI in n 1536750498.965 * [misc]backup-simplify: Simplify PI into PI 1536750498.965 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750498.965 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536750498.966 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750498.967 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536750498.968 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750498.968 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750498.968 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750498.968 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750498.969 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750498.970 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1536750498.971 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1536750498.971 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 1536750498.971 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536750498.971 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750498.971 * [misc]taylor: Taking taylor expansion of k in n 1536750498.971 * [misc]backup-simplify: Simplify k into k 1536750498.971 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750498.971 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536750498.971 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750498.971 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536750498.971 * [misc]taylor: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 1536750498.971 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 1536750498.972 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 1536750498.972 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750498.972 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.972 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.972 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750498.972 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750498.972 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.972 * [misc]taylor: Taking taylor expansion of k in n 1536750498.972 * [misc]backup-simplify: Simplify k into k 1536750498.972 * [misc]taylor: Taking taylor expansion of (log (* 2 (* n PI))) in n 1536750498.972 * [misc]taylor: Taking taylor expansion of (* 2 (* n PI)) in n 1536750498.972 * [misc]taylor: Taking taylor expansion of 2 in n 1536750498.972 * [misc]backup-simplify: Simplify 2 into 2 1536750498.972 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750498.972 * [misc]taylor: Taking taylor expansion of n in n 1536750498.972 * [misc]backup-simplify: Simplify 0 into 0 1536750498.972 * [misc]backup-simplify: Simplify 1 into 1 1536750498.972 * [misc]taylor: Taking taylor expansion of PI in n 1536750498.972 * [misc]backup-simplify: Simplify PI into PI 1536750498.972 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750498.973 * [misc]backup-simplify: Simplify (* 2 0) into 0 1536750498.973 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750498.974 * [misc]backup-simplify: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 1536750498.975 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750498.975 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750498.975 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750498.975 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750498.976 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750498.976 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 1536750498.977 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 1536750498.978 * [misc]backup-simplify: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) 1536750498.978 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 1536750498.978 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 1536750498.978 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 1536750498.978 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750498.978 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.978 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.978 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750498.978 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750498.978 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750498.978 * [misc]taylor: Taking taylor expansion of k in k 1536750498.978 * [misc]backup-simplify: Simplify 0 into 0 1536750498.979 * [misc]backup-simplify: Simplify 1 into 1 1536750498.979 * [misc]taylor: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 1536750498.979 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750498.979 * [misc]taylor: Taking taylor expansion of n in k 1536750498.979 * [misc]backup-simplify: Simplify n into n 1536750498.979 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750498.979 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536750498.979 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536750498.979 * [misc]taylor: Taking taylor expansion of 2 in k 1536750498.979 * [misc]backup-simplify: Simplify 2 into 2 1536750498.979 * [misc]taylor: Taking taylor expansion of PI in k 1536750498.979 * [misc]backup-simplify: Simplify PI into PI 1536750498.979 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750498.980 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750498.980 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750498.980 * [misc]backup-simplify: Simplify (- 0) into 0 1536750498.980 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750498.981 * [misc]backup-simplify: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750498.982 * [misc]backup-simplify: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 1536750498.982 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 1536750498.982 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536750498.982 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750498.982 * [misc]taylor: Taking taylor expansion of k in k 1536750498.982 * [misc]backup-simplify: Simplify 0 into 0 1536750498.982 * [misc]backup-simplify: Simplify 1 into 1 1536750498.982 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750498.983 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750498.983 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750498.984 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 1536750498.984 * [misc]backup-simplify: Simplify 0 into 0 1536750498.985 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536750498.986 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 1536750498.989 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536750498.989 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536750498.990 * [misc]backup-simplify: Simplify (- 0) into 0 1536750498.990 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750498.991 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750498.991 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 1536750498.993 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750498.994 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 1536750498.994 * [misc]taylor: Taking taylor expansion of 0 in k 1536750498.994 * [misc]backup-simplify: Simplify 0 into 0 1536750498.995 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536750498.996 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536750498.999 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536750498.999 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750498.999 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536750498.999 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750498.999 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750499.000 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1536750499.002 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536750499.005 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536750499.005 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536750499.007 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750499.009 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1536750499.015 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536750499.015 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536750499.015 * [misc]backup-simplify: Simplify (- 0) into 0 1536750499.015 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750499.016 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750499.017 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536750499.019 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750499.020 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750499.020 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1536750499.021 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 1536750499.022 * [misc]taylor: Taking taylor expansion of 0 in k 1536750499.022 * [misc]backup-simplify: Simplify 0 into 0 1536750499.022 * [misc]backup-simplify: Simplify 0 into 0 1536750499.022 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536750499.023 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750499.025 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536750499.026 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536750499.032 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536750499.032 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750499.033 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536750499.033 * [misc]backup-simplify: Simplify (- 0) into 0 1536750499.033 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750499.034 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 1536750499.038 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 1536750499.044 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 1536750499.047 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 1536750499.050 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536750499.052 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1536750499.059 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536750499.059 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1536750499.059 * [misc]backup-simplify: Simplify (- 0) into 0 1536750499.059 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750499.060 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 1536750499.060 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1536750499.063 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750499.063 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750499.063 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1536750499.064 * [misc]backup-simplify: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 1536750499.064 * [misc]taylor: Taking taylor expansion of 0 in k 1536750499.064 * [misc]backup-simplify: Simplify 0 into 0 1536750499.064 * [misc]backup-simplify: Simplify 0 into 0 1536750499.064 * [misc]backup-simplify: Simplify 0 into 0 1536750499.064 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750499.065 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750499.067 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 1536750499.068 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750499.073 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536750499.074 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750499.074 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536750499.074 * [misc]backup-simplify: Simplify (- 0) into 0 1536750499.074 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750499.075 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 1536750499.080 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 1536750499.093 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 1536750499.101 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 1536750499.112 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 1536750499.112 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* (/ 1 n) PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536750499.112 * [misc]approximate: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 1536750499.112 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536750499.112 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536750499.112 * [misc]taylor: Taking taylor expansion of k in k 1536750499.112 * [misc]backup-simplify: Simplify 0 into 0 1536750499.112 * [misc]backup-simplify: Simplify 1 into 1 1536750499.113 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750499.113 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750499.113 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750499.113 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 1536750499.113 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 1536750499.113 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750499.113 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750499.113 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.113 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750499.113 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750499.113 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.113 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750499.113 * [misc]taylor: Taking taylor expansion of k in k 1536750499.113 * [misc]backup-simplify: Simplify 0 into 0 1536750499.113 * [misc]backup-simplify: Simplify 1 into 1 1536750499.113 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750499.113 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1536750499.113 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in k 1536750499.113 * [misc]taylor: Taking taylor expansion of 2 in k 1536750499.113 * [misc]backup-simplify: Simplify 2 into 2 1536750499.113 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750499.113 * [misc]taylor: Taking taylor expansion of PI in k 1536750499.113 * [misc]backup-simplify: Simplify PI into PI 1536750499.113 * [misc]taylor: Taking taylor expansion of n in k 1536750499.113 * [misc]backup-simplify: Simplify n into n 1536750499.113 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750499.113 * [misc]backup-simplify: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 1536750499.114 * [misc]backup-simplify: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 1536750499.114 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750499.114 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750499.114 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750499.114 * [misc]backup-simplify: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 1536750499.114 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536750499.114 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750499.114 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536750499.114 * [misc]taylor: Taking taylor expansion of k in n 1536750499.114 * [misc]backup-simplify: Simplify k into k 1536750499.114 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536750499.114 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536750499.114 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750499.114 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536750499.114 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536750499.114 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750499.114 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750499.114 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.114 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750499.114 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750499.114 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.114 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750499.114 * [misc]taylor: Taking taylor expansion of k in n 1536750499.115 * [misc]backup-simplify: Simplify k into k 1536750499.115 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750499.115 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536750499.115 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536750499.115 * [misc]taylor: Taking taylor expansion of 2 in n 1536750499.115 * [misc]backup-simplify: Simplify 2 into 2 1536750499.115 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750499.115 * [misc]taylor: Taking taylor expansion of PI in n 1536750499.115 * [misc]backup-simplify: Simplify PI into PI 1536750499.115 * [misc]taylor: Taking taylor expansion of n in n 1536750499.115 * [misc]backup-simplify: Simplify 0 into 0 1536750499.115 * [misc]backup-simplify: Simplify 1 into 1 1536750499.115 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750499.115 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750499.115 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750499.116 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750499.116 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750499.116 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750499.116 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750499.117 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1536750499.117 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536750499.117 * [misc]taylor: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750499.117 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536750499.117 * [misc]taylor: Taking taylor expansion of k in n 1536750499.117 * [misc]backup-simplify: Simplify k into k 1536750499.117 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536750499.117 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536750499.117 * [misc]taylor: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750499.118 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 1536750499.118 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 1536750499.118 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750499.118 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750499.118 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.118 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750499.118 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750499.118 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.118 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750499.118 * [misc]taylor: Taking taylor expansion of k in n 1536750499.118 * [misc]backup-simplify: Simplify k into k 1536750499.118 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750499.118 * [misc]taylor: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1536750499.118 * [misc]taylor: Taking taylor expansion of (* 2 (/ PI n)) in n 1536750499.118 * [misc]taylor: Taking taylor expansion of 2 in n 1536750499.118 * [misc]backup-simplify: Simplify 2 into 2 1536750499.118 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750499.118 * [misc]taylor: Taking taylor expansion of PI in n 1536750499.118 * [misc]backup-simplify: Simplify PI into PI 1536750499.118 * [misc]taylor: Taking taylor expansion of n in n 1536750499.118 * [misc]backup-simplify: Simplify 0 into 0 1536750499.118 * [misc]backup-simplify: Simplify 1 into 1 1536750499.118 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750499.118 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750499.119 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750499.119 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750499.119 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750499.119 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750499.119 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750499.120 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 1536750499.120 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536750499.121 * [misc]backup-simplify: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) 1536750499.121 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 1536750499.121 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 1536750499.121 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 1536750499.121 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750499.121 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750499.121 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.121 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750499.121 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750499.121 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.121 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750499.121 * [misc]taylor: Taking taylor expansion of k in k 1536750499.121 * [misc]backup-simplify: Simplify 0 into 0 1536750499.121 * [misc]backup-simplify: Simplify 1 into 1 1536750499.121 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750499.121 * [misc]taylor: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 1536750499.121 * [misc]taylor: Taking taylor expansion of (log (* 2 PI)) in k 1536750499.121 * [misc]taylor: Taking taylor expansion of (* 2 PI) in k 1536750499.121 * [misc]taylor: Taking taylor expansion of 2 in k 1536750499.121 * [misc]backup-simplify: Simplify 2 into 2 1536750499.121 * [misc]taylor: Taking taylor expansion of PI in k 1536750499.121 * [misc]backup-simplify: Simplify PI into PI 1536750499.121 * [misc]backup-simplify: Simplify (* 2 PI) into (* 2 PI) 1536750499.122 * [misc]backup-simplify: Simplify (log (* 2 PI)) into (log (* 2 PI)) 1536750499.122 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750499.122 * [misc]taylor: Taking taylor expansion of n in k 1536750499.122 * [misc]backup-simplify: Simplify n into n 1536750499.122 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750499.122 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750499.122 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750499.122 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750499.122 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536750499.123 * [misc]backup-simplify: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 1536750499.123 * [misc]backup-simplify: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 1536750499.123 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 1536750499.124 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536750499.124 * [misc]taylor: Taking taylor expansion of k in k 1536750499.124 * [misc]backup-simplify: Simplify 0 into 0 1536750499.124 * [misc]backup-simplify: Simplify 1 into 1 1536750499.124 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750499.124 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750499.124 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 1536750499.124 * [misc]backup-simplify: Simplify 0 into 0 1536750499.126 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750499.126 * [misc]backup-simplify: Simplify (+ (* 2 0) (* 0 PI)) into 0 1536750499.128 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 1536750499.128 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750499.128 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750499.128 * [misc]backup-simplify: Simplify (- 0) into 0 1536750499.128 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750499.129 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750499.129 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 1536750499.130 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750499.131 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 1536750499.131 * [misc]taylor: Taking taylor expansion of 0 in k 1536750499.131 * [misc]backup-simplify: Simplify 0 into 0 1536750499.131 * [misc]backup-simplify: Simplify 0 into 0 1536750499.132 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536750499.132 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536750499.133 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750499.134 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 1536750499.137 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 1536750499.137 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750499.138 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750499.138 * [misc]backup-simplify: Simplify (- 0) into 0 1536750499.138 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750499.138 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750499.139 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 1536750499.140 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750499.141 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1536750499.141 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 1536750499.141 * [misc]taylor: Taking taylor expansion of 0 in k 1536750499.141 * [misc]backup-simplify: Simplify 0 into 0 1536750499.141 * [misc]backup-simplify: Simplify 0 into 0 1536750499.141 * [misc]backup-simplify: Simplify 0 into 0 1536750499.142 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750499.143 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536750499.143 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536750499.145 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750499.146 * [misc]backup-simplify: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750499.151 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 1536750499.151 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750499.152 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536750499.152 * [misc]backup-simplify: Simplify (- 0) into 0 1536750499.152 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750499.153 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 1536750499.154 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 1536750499.158 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750499.158 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1536750499.159 * [misc]backup-simplify: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 1536750499.159 * [misc]taylor: Taking taylor expansion of 0 in k 1536750499.160 * [misc]backup-simplify: Simplify 0 into 0 1536750499.160 * [misc]backup-simplify: Simplify 0 into 0 1536750499.160 * [misc]backup-simplify: Simplify 0 into 0 1536750499.160 * [misc]backup-simplify: Simplify 0 into 0 1536750499.161 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750499.162 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536750499.163 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 1536750499.167 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 1536750499.167 * [misc]backup-simplify: Simplify (/ (pow (* 2 (* (/ 1 (- n)) PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1536750499.167 * [misc]approximate: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1536750499.167 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1536750499.167 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750499.167 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 1536750499.167 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 1536750499.167 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750499.167 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750499.168 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750499.168 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.168 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750499.168 * [misc]taylor: Taking taylor expansion of k in k 1536750499.168 * [misc]backup-simplify: Simplify 0 into 0 1536750499.168 * [misc]backup-simplify: Simplify 1 into 1 1536750499.168 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750499.168 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750499.168 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.168 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1536750499.168 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in k 1536750499.168 * [misc]taylor: Taking taylor expansion of -2 in k 1536750499.168 * [misc]backup-simplify: Simplify -2 into -2 1536750499.168 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750499.168 * [misc]taylor: Taking taylor expansion of PI in k 1536750499.168 * [misc]backup-simplify: Simplify PI into PI 1536750499.168 * [misc]taylor: Taking taylor expansion of n in k 1536750499.168 * [misc]backup-simplify: Simplify n into n 1536750499.168 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750499.168 * [misc]backup-simplify: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 1536750499.169 * [misc]backup-simplify: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 1536750499.169 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750499.169 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750499.169 * [misc]backup-simplify: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 1536750499.169 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750499.170 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536750499.170 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536750499.170 * [misc]taylor: Taking taylor expansion of -1 in k 1536750499.170 * [misc]backup-simplify: Simplify -1 into -1 1536750499.170 * [misc]taylor: Taking taylor expansion of k in k 1536750499.170 * [misc]backup-simplify: Simplify 0 into 0 1536750499.170 * [misc]backup-simplify: Simplify 1 into 1 1536750499.170 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750499.170 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750499.171 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536750499.171 * [misc]backup-simplify: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750499.171 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1536750499.171 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750499.171 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536750499.171 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536750499.171 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750499.171 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750499.171 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750499.171 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.171 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750499.171 * [misc]taylor: Taking taylor expansion of k in n 1536750499.172 * [misc]backup-simplify: Simplify k into k 1536750499.172 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750499.172 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750499.172 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.172 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536750499.172 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536750499.172 * [misc]taylor: Taking taylor expansion of -2 in n 1536750499.172 * [misc]backup-simplify: Simplify -2 into -2 1536750499.172 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750499.172 * [misc]taylor: Taking taylor expansion of PI in n 1536750499.172 * [misc]backup-simplify: Simplify PI into PI 1536750499.172 * [misc]taylor: Taking taylor expansion of n in n 1536750499.172 * [misc]backup-simplify: Simplify 0 into 0 1536750499.172 * [misc]backup-simplify: Simplify 1 into 1 1536750499.172 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750499.173 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536750499.173 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536750499.173 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750499.173 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750499.174 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750499.175 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1536750499.176 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536750499.176 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536750499.176 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536750499.176 * [misc]taylor: Taking taylor expansion of -1 in n 1536750499.176 * [misc]backup-simplify: Simplify -1 into -1 1536750499.176 * [misc]taylor: Taking taylor expansion of k in n 1536750499.176 * [misc]backup-simplify: Simplify k into k 1536750499.176 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536750499.176 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536750499.176 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536750499.176 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536750499.177 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 1536750499.177 * [misc]taylor: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1536750499.177 * [misc]taylor: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750499.177 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 1536750499.177 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 1536750499.177 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750499.177 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750499.177 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750499.177 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.177 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750499.177 * [misc]taylor: Taking taylor expansion of k in n 1536750499.177 * [misc]backup-simplify: Simplify k into k 1536750499.177 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750499.177 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750499.178 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.178 * [misc]taylor: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1536750499.178 * [misc]taylor: Taking taylor expansion of (* -2 (/ PI n)) in n 1536750499.178 * [misc]taylor: Taking taylor expansion of -2 in n 1536750499.178 * [misc]backup-simplify: Simplify -2 into -2 1536750499.178 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750499.178 * [misc]taylor: Taking taylor expansion of PI in n 1536750499.178 * [misc]backup-simplify: Simplify PI into PI 1536750499.178 * [misc]taylor: Taking taylor expansion of n in n 1536750499.178 * [misc]backup-simplify: Simplify 0 into 0 1536750499.178 * [misc]backup-simplify: Simplify 1 into 1 1536750499.178 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750499.178 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536750499.180 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536750499.180 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750499.180 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750499.180 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750499.181 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 1536750499.182 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536750499.182 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536750499.182 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536750499.182 * [misc]taylor: Taking taylor expansion of -1 in n 1536750499.182 * [misc]backup-simplify: Simplify -1 into -1 1536750499.182 * [misc]taylor: Taking taylor expansion of k in n 1536750499.182 * [misc]backup-simplify: Simplify k into k 1536750499.182 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536750499.182 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536750499.182 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536750499.183 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536750499.183 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 1536750499.183 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 1536750499.183 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 1536750499.184 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 1536750499.184 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750499.184 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750499.184 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750499.184 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.184 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750499.184 * [misc]taylor: Taking taylor expansion of k in k 1536750499.184 * [misc]backup-simplify: Simplify 0 into 0 1536750499.184 * [misc]backup-simplify: Simplify 1 into 1 1536750499.184 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750499.184 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750499.184 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750499.184 * [misc]taylor: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 1536750499.184 * [misc]taylor: Taking taylor expansion of (log (* -2 PI)) in k 1536750499.184 * [misc]taylor: Taking taylor expansion of (* -2 PI) in k 1536750499.184 * [misc]taylor: Taking taylor expansion of -2 in k 1536750499.184 * [misc]backup-simplify: Simplify -2 into -2 1536750499.184 * [misc]taylor: Taking taylor expansion of PI in k 1536750499.184 * [misc]backup-simplify: Simplify PI into PI 1536750499.184 * [misc]backup-simplify: Simplify (* -2 PI) into (* -2 PI) 1536750499.185 * [misc]backup-simplify: Simplify (log (* -2 PI)) into (log (* -2 PI)) 1536750499.185 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750499.185 * [misc]taylor: Taking taylor expansion of n in k 1536750499.185 * [misc]backup-simplify: Simplify n into n 1536750499.185 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750499.185 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750499.186 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750499.186 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536750499.186 * [misc]backup-simplify: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 1536750499.187 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 1536750499.187 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 1536750499.188 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536750499.188 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536750499.188 * [misc]taylor: Taking taylor expansion of -1 in k 1536750499.188 * [misc]backup-simplify: Simplify -1 into -1 1536750499.188 * [misc]taylor: Taking taylor expansion of k in k 1536750499.188 * [misc]backup-simplify: Simplify 0 into 0 1536750499.188 * [misc]backup-simplify: Simplify 1 into 1 1536750499.188 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750499.188 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750499.188 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536750499.189 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1536750499.190 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 1536750499.191 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750499.192 * [misc]backup-simplify: Simplify (+ (* -2 0) (* 0 PI)) into 0 1536750499.195 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 1536750499.195 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750499.195 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750499.196 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750499.196 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750499.197 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 1536750499.199 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750499.200 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1536750499.200 * [misc]taylor: Taking taylor expansion of 0 in k 1536750499.200 * [misc]backup-simplify: Simplify 0 into 0 1536750499.200 * [misc]backup-simplify: Simplify 0 into 0 1536750499.200 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536750499.201 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750499.203 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1536750499.203 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1536750499.205 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750499.206 * [misc]backup-simplify: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 1536750499.212 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 1536750499.212 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750499.213 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750499.213 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750499.216 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 1536750499.217 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 1536750499.219 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750499.220 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750499.220 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1536750499.222 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1536750499.222 * [misc]taylor: Taking taylor expansion of 0 in k 1536750499.222 * [misc]backup-simplify: Simplify 0 into 0 1536750499.222 * [misc]backup-simplify: Simplify 0 into 0 1536750499.222 * [misc]backup-simplify: Simplify 0 into 0 1536750499.222 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750499.223 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750499.225 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1536750499.226 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 1536750499.230 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 1536750499.230 * * * [misc]progress: simplifying candidates 1536750499.230 * * * * [misc]progress: [ 1 / 76 ] simplifiying candidate # 1536750499.230 * [enter]simplify: Simplifying (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) 1536750499.231 * * [misc]simplify: iters left: 6 (11 enodes) 1536750499.238 * * [misc]simplify: iters left: 5 (21 enodes) 1536750499.249 * * [misc]simplify: iters left: 4 (47 enodes) 1536750499.275 * * [misc]simplify: iters left: 3 (109 enodes) 1536750499.358 * * [misc]simplify: iters left: 2 (300 enodes) 1536750499.668 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* (* PI n) 2))) 1536750499.668 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (exp (* (- 1/2 (/ k 2)) (log (* (* PI n) 2)))) (sqrt k))) 1536750499.668 * * * * [misc]progress: [ 2 / 76 ] simplifiying candidate # 1536750499.668 * * * * [misc]progress: [ 3 / 76 ] simplifiying candidate # 1536750499.668 * [enter]simplify: Simplifying (* 2 (* n PI)) 1536750499.669 * * [misc]simplify: iters left: 4 (5 enodes) 1536750499.670 * * [misc]simplify: iters left: 3 (9 enodes) 1536750499.672 * * [misc]simplify: iters left: 2 (15 enodes) 1536750499.675 * * [misc]simplify: iters left: 1 (17 enodes) 1536750499.678 * [exit]simplify: Simplified to (* (* PI n) 2) 1536750499.678 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (pow (* (* PI n) 2) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) 1536750499.678 * * * * [misc]progress: [ 4 / 76 ] simplifiying candidate # 1536750499.678 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) (/ k 2)) 1536750499.679 * * [misc]simplify: iters left: 5 (8 enodes) 1536750499.681 * * [misc]simplify: iters left: 4 (12 enodes) 1536750499.684 * * [misc]simplify: iters left: 3 (18 enodes) 1536750499.687 * * [misc]simplify: iters left: 2 (20 enodes) 1536750499.693 * [exit]simplify: Simplified to (pow (* (* PI n) 2) (/ k 2)) 1536750499.693 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (/ (pow (* 2 (* n PI)) 1/2) (pow (* (* PI n) 2) (/ k 2))) (sqrt k))) 1536750499.693 * * * * [misc]progress: [ 5 / 76 ] simplifiying candidate # 1536750499.694 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1536750499.694 * * [misc]simplify: iters left: 5 (6 enodes) 1536750499.696 * * [misc]simplify: iters left: 4 (8 enodes) 1536750499.699 * * [misc]simplify: iters left: 3 (11 enodes) 1536750499.702 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1536750499.702 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* 2 (* n PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))) 1536750499.702 * * * * [misc]progress: [ 6 / 76 ] simplifiying candidate # 1536750499.703 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1536750499.703 * * [misc]simplify: iters left: 5 (6 enodes) 1536750499.705 * * [misc]simplify: iters left: 4 (8 enodes) 1536750499.708 * * [misc]simplify: iters left: 3 (11 enodes) 1536750499.711 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1536750499.711 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* 2 (* n PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))) 1536750499.711 * * * * [misc]progress: [ 7 / 76 ] simplifiying candidate # 1536750499.711 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1536750499.712 * * [misc]simplify: iters left: 4 (5 enodes) 1536750499.714 * * [misc]simplify: iters left: 3 (7 enodes) 1536750499.716 * * [misc]simplify: iters left: 2 (10 enodes) 1536750499.719 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1536750499.719 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (pow (pow (* 2 (* n PI)) 1) (- 1/2 (/ k 2))) (sqrt k))) 1536750499.719 * * * * [misc]progress: [ 8 / 76 ] simplifiying candidate # 1536750499.719 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) (- (/ k 2))) 1536750499.720 * * [misc]simplify: iters left: 5 (9 enodes) 1536750499.724 * * [misc]simplify: iters left: 4 (15 enodes) 1536750499.726 * * [misc]simplify: iters left: 3 (21 enodes) 1536750499.730 * * [misc]simplify: iters left: 2 (22 enodes) 1536750499.733 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- (/ k 2))) 1536750499.733 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* 2 (* n PI)) 1/2) (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k))) 1536750499.733 * * * * [misc]progress: [ 9 / 76 ] simplifiying candidate # 1536750499.733 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) (- (/ k 2))) 1536750499.734 * * [misc]simplify: iters left: 5 (9 enodes) 1536750499.736 * * [misc]simplify: iters left: 4 (15 enodes) 1536750499.739 * * [misc]simplify: iters left: 3 (21 enodes) 1536750499.742 * * [misc]simplify: iters left: 2 (22 enodes) 1536750499.745 * [exit]simplify: Simplified to (pow (* (* 2 n) PI) (- (/ k 2))) 1536750499.745 * [misc]simplify: Simplified (2 1 2) to (λ (k n) (/ (* (pow (* 2 (* n PI)) 1/2) (pow (* (* 2 n) PI) (- (/ k 2)))) (sqrt k))) 1536750499.745 * * * * [misc]progress: [ 10 / 76 ] simplifiying candidate # 1536750499.745 * [enter]simplify: Simplifying (pow 2 (- 1/2 (/ k 2))) 1536750499.746 * * [misc]simplify: iters left: 5 (6 enodes) 1536750499.747 * * [misc]simplify: iters left: 4 (8 enodes) 1536750499.748 * * [misc]simplify: iters left: 3 (11 enodes) 1536750499.750 * [exit]simplify: Simplified to (pow 2 (- 1/2 (/ k 2))) 1536750499.750 * [misc]simplify: Simplified (2 1 1) to (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))) 1536750499.750 * * * * [misc]progress: [ 11 / 76 ] simplifiying candidate # 1536750499.750 * * * * [misc]progress: [ 12 / 76 ] simplifiying candidate # 1536750499.750 * * * * [misc]progress: [ 13 / 76 ] simplifiying candidate # 1536750499.750 * * * * [misc]progress: [ 14 / 76 ] simplifiying candidate # 1536750499.750 * * * * [misc]progress: [ 15 / 76 ] simplifiying candidate # 1536750499.750 * * * * [misc]progress: [ 16 / 76 ] simplifiying candidate # 1536750499.750 * * * * [misc]progress: [ 17 / 76 ] simplifiying candidate # 1536750499.750 * * * * [misc]progress: [ 18 / 76 ] simplifiying candidate # 1536750499.750 * * * * [misc]progress: [ 19 / 76 ] simplifiying candidate # 1536750499.750 * * * * [misc]progress: [ 20 / 76 ] simplifiying candidate # 1536750499.750 * * * * [misc]progress: [ 21 / 76 ] simplifiying candidate # 1536750499.750 * * * * [misc]progress: [ 22 / 76 ] simplifiying candidate # 1536750499.750 * * * * [misc]progress: [ 23 / 76 ] simplifiying candidate # 1536750499.750 * * * * [misc]progress: [ 24 / 76 ] simplifiying candidate # 1536750499.750 * * * * [misc]progress: [ 25 / 76 ] simplifiying candidate # 1536750499.750 * * * * [misc]progress: [ 26 / 76 ] simplifiying candidate # 1536750499.751 * * * * [misc]progress: [ 27 / 76 ] simplifiying candidate # 1536750499.751 * [enter]simplify: Simplifying (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750499.752 * * [misc]simplify: iters left: 6 (14 enodes) 1536750499.759 * * [misc]simplify: iters left: 5 (26 enodes) 1536750499.770 * * [misc]simplify: iters left: 4 (53 enodes) 1536750499.804 * * [misc]simplify: iters left: 3 (137 enodes) 1536750499.899 * * [misc]simplify: iters left: 2 (487 enodes) 1536750500.857 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k))) 1536750500.857 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k))))) 1536750500.857 * * * * [misc]progress: [ 28 / 76 ] simplifiying candidate # 1536750500.858 * [enter]simplify: Simplifying (- (* (log (* 2 (* n PI))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750500.859 * * [misc]simplify: iters left: 6 (14 enodes) 1536750500.866 * * [misc]simplify: iters left: 5 (26 enodes) 1536750500.880 * * [misc]simplify: iters left: 4 (53 enodes) 1536750500.907 * * [misc]simplify: iters left: 3 (137 enodes) 1536750500.996 * * [misc]simplify: iters left: 2 (487 enodes) 1536750502.293 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k))) 1536750502.293 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (log (* (* PI n) 2))) (log (sqrt k))))) 1536750502.293 * * * * [misc]progress: [ 29 / 76 ] simplifiying candidate # 1536750502.294 * [enter]simplify: Simplifying (- (log (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (log (sqrt k))) 1536750502.295 * * [misc]simplify: iters left: 6 (14 enodes) 1536750502.302 * * [misc]simplify: iters left: 5 (24 enodes) 1536750502.312 * * [misc]simplify: iters left: 4 (42 enodes) 1536750502.329 * * [misc]simplify: iters left: 3 (71 enodes) 1536750502.379 * * [misc]simplify: iters left: 2 (208 enodes) 1536750502.773 * [exit]simplify: Simplified to (- (* (log (* (* PI n) 2)) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750502.773 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (log (* (* PI n) 2)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536750502.773 * * * * [misc]progress: [ 30 / 76 ] simplifiying candidate # 1536750502.773 * * * * [misc]progress: [ 31 / 76 ] simplifiying candidate # 1536750502.773 * * * * [misc]progress: [ 32 / 76 ] simplifiying candidate # 1536750502.774 * [enter]simplify: Simplifying (/ (* (* (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1536750502.775 * * [misc]simplify: iters left: 6 (16 enodes) 1536750502.783 * * [misc]simplify: iters left: 5 (31 enodes) 1536750502.791 * * [misc]simplify: iters left: 4 (67 enodes) 1536750502.808 * * [misc]simplify: iters left: 3 (124 enodes) 1536750502.843 * * [misc]simplify: iters left: 2 (195 enodes) 1536750502.934 * * [misc]simplify: iters left: 1 (309 enodes) 1536750503.103 * [exit]simplify: Simplified to (* (* (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (* k (sqrt k)))) 1536750503.103 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (* k (sqrt k)))))) 1536750503.103 * * * * [misc]progress: [ 33 / 76 ] simplifiying candidate # 1536750503.103 * * * * [misc]progress: [ 34 / 76 ] simplifiying candidate # 1536750503.103 * * * * [misc]progress: [ 35 / 76 ] simplifiying candidate # 1536750503.103 * * * * [misc]progress: [ 36 / 76 ] simplifiying candidate # 1536750503.103 * * * * [misc]progress: [ 37 / 76 ] simplifiying candidate # 1536750503.103 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750503.104 * * [misc]simplify: iters left: 6 (12 enodes) 1536750503.107 * * [misc]simplify: iters left: 5 (19 enodes) 1536750503.110 * * [misc]simplify: iters left: 4 (25 enodes) 1536750503.114 * * [misc]simplify: iters left: 3 (26 enodes) 1536750503.118 * [exit]simplify: Simplified to (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750503.118 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k))))) 1536750503.118 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k))) 1536750503.119 * * [misc]simplify: iters left: 6 (12 enodes) 1536750503.122 * * [misc]simplify: iters left: 5 (18 enodes) 1536750503.125 * * [misc]simplify: iters left: 4 (24 enodes) 1536750503.129 * * [misc]simplify: iters left: 3 (25 enodes) 1536750503.133 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- (/ k 2))) (cbrt (sqrt k))) 1536750503.133 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI n) 2) (- (/ k 2))) (cbrt (sqrt k))))) 1536750503.133 * * * * [misc]progress: [ 38 / 76 ] simplifiying candidate # 1536750503.133 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k))) 1536750503.133 * * [misc]simplify: iters left: 6 (11 enodes) 1536750503.136 * * [misc]simplify: iters left: 5 (16 enodes) 1536750503.138 * * [misc]simplify: iters left: 4 (22 enodes) 1536750503.142 * * [misc]simplify: iters left: 3 (24 enodes) 1536750503.145 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) 1536750503.145 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k))))) 1536750503.146 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k))) 1536750503.146 * * [misc]simplify: iters left: 6 (12 enodes) 1536750503.149 * * [misc]simplify: iters left: 5 (18 enodes) 1536750503.152 * * [misc]simplify: iters left: 4 (24 enodes) 1536750503.155 * * [misc]simplify: iters left: 3 (25 enodes) 1536750503.159 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt (sqrt k))) 1536750503.159 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt (sqrt k))))) 1536750503.160 * * * * [misc]progress: [ 39 / 76 ] simplifiying candidate # 1536750503.160 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) 1/2) 1) 1536750503.160 * * [misc]simplify: iters left: 6 (9 enodes) 1536750503.162 * * [misc]simplify: iters left: 5 (16 enodes) 1536750503.166 * * [misc]simplify: iters left: 4 (24 enodes) 1536750503.171 * * [misc]simplify: iters left: 3 (26 enodes) 1536750503.177 * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) 1536750503.177 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k)))) 1536750503.177 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k)) 1536750503.178 * * [misc]simplify: iters left: 6 (11 enodes) 1536750503.183 * * [misc]simplify: iters left: 5 (17 enodes) 1536750503.189 * * [misc]simplify: iters left: 4 (23 enodes) 1536750503.196 * * [misc]simplify: iters left: 3 (24 enodes) 1536750503.204 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)) 1536750503.204 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)))) 1536750503.204 * * * * [misc]progress: [ 40 / 76 ] simplifiying candidate # 1536750503.205 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750503.206 * * [misc]simplify: iters left: 6 (12 enodes) 1536750503.211 * * [misc]simplify: iters left: 5 (19 enodes) 1536750503.218 * * [misc]simplify: iters left: 4 (25 enodes) 1536750503.226 * * [misc]simplify: iters left: 3 (26 enodes) 1536750503.234 * [exit]simplify: Simplified to (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750503.235 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k))))) 1536750503.235 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (cbrt (sqrt k))) 1536750503.236 * * [misc]simplify: iters left: 6 (12 enodes) 1536750503.241 * * [misc]simplify: iters left: 5 (18 enodes) 1536750503.245 * * [misc]simplify: iters left: 4 (24 enodes) 1536750503.249 * * [misc]simplify: iters left: 3 (25 enodes) 1536750503.253 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- (/ k 2))) (cbrt (sqrt k))) 1536750503.253 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* PI n) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI n) 2) (- (/ k 2))) (cbrt (sqrt k))))) 1536750503.253 * * * * [misc]progress: [ 41 / 76 ] simplifiying candidate # 1536750503.253 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) 1/2) (sqrt (sqrt k))) 1536750503.254 * * [misc]simplify: iters left: 6 (11 enodes) 1536750503.256 * * [misc]simplify: iters left: 5 (16 enodes) 1536750503.258 * * [misc]simplify: iters left: 4 (22 enodes) 1536750503.262 * * [misc]simplify: iters left: 3 (24 enodes) 1536750503.266 * [exit]simplify: Simplified to (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) 1536750503.266 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k))))) 1536750503.267 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt (sqrt k))) 1536750503.268 * * [misc]simplify: iters left: 6 (12 enodes) 1536750503.270 * * [misc]simplify: iters left: 5 (18 enodes) 1536750503.274 * * [misc]simplify: iters left: 4 (24 enodes) 1536750503.281 * * [misc]simplify: iters left: 3 (25 enodes) 1536750503.289 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt (sqrt k))) 1536750503.289 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt (sqrt k))))) 1536750503.289 * * * * [misc]progress: [ 42 / 76 ] simplifiying candidate # 1536750503.290 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) 1/2) 1) 1536750503.290 * * [misc]simplify: iters left: 6 (9 enodes) 1536750503.294 * * [misc]simplify: iters left: 5 (16 enodes) 1536750503.301 * * [misc]simplify: iters left: 4 (24 enodes) 1536750503.307 * * [misc]simplify: iters left: 3 (26 enodes) 1536750503.314 * [exit]simplify: Simplified to (sqrt (* (* 2 PI) n)) 1536750503.314 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k)))) 1536750503.314 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- (/ k 2))) (sqrt k)) 1536750503.315 * * [misc]simplify: iters left: 6 (11 enodes) 1536750503.320 * * [misc]simplify: iters left: 5 (17 enodes) 1536750503.326 * * [misc]simplify: iters left: 4 (23 enodes) 1536750503.332 * * [misc]simplify: iters left: 3 (24 enodes) 1536750503.340 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)) 1536750503.340 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (* (* 2 PI) n)) (/ (pow (* (* PI n) 2) (- (/ k 2))) (sqrt k)))) 1536750503.340 * * * * [misc]progress: [ 43 / 76 ] simplifiying candidate # 1536750503.340 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750503.341 * * [misc]simplify: iters left: 6 (10 enodes) 1536750503.345 * * [misc]simplify: iters left: 5 (14 enodes) 1536750503.350 * * [misc]simplify: iters left: 4 (17 enodes) 1536750503.355 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750503.355 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536750503.356 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750503.357 * * [misc]simplify: iters left: 6 (12 enodes) 1536750503.361 * * [misc]simplify: iters left: 5 (15 enodes) 1536750503.365 * * [misc]simplify: iters left: 4 (18 enodes) 1536750503.369 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750503.370 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536750503.370 * * * * [misc]progress: [ 44 / 76 ] simplifiying candidate # 1536750503.370 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750503.370 * * [misc]simplify: iters left: 6 (9 enodes) 1536750503.372 * * [misc]simplify: iters left: 5 (11 enodes) 1536750503.374 * * [misc]simplify: iters left: 4 (14 enodes) 1536750503.376 * [exit]simplify: Simplified to (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750503.376 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536750503.376 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750503.377 * * [misc]simplify: iters left: 6 (12 enodes) 1536750503.379 * * [misc]simplify: iters left: 5 (15 enodes) 1536750503.381 * * [misc]simplify: iters left: 4 (18 enodes) 1536750503.384 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750503.384 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (pow 2 (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536750503.384 * * * * [misc]progress: [ 45 / 76 ] simplifiying candidate # 1536750503.384 * [enter]simplify: Simplifying (/ (pow 2 (- 1/2 (/ k 2))) 1) 1536750503.384 * * [misc]simplify: iters left: 6 (8 enodes) 1536750503.386 * * [misc]simplify: iters left: 5 (12 enodes) 1536750503.388 * * [misc]simplify: iters left: 4 (17 enodes) 1536750503.390 * [exit]simplify: Simplified to (pow 2 (- 1/2 (/ k 2))) 1536750503.390 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536750503.391 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536750503.392 * * [misc]simplify: iters left: 6 (11 enodes) 1536750503.394 * * [misc]simplify: iters left: 5 (14 enodes) 1536750503.396 * * [misc]simplify: iters left: 4 (17 enodes) 1536750503.399 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536750503.399 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536750503.399 * * * * [misc]progress: [ 46 / 76 ] simplifiying candidate # 1536750503.399 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750503.400 * * [misc]simplify: iters left: 6 (16 enodes) 1536750503.404 * * [misc]simplify: iters left: 5 (28 enodes) 1536750503.412 * * [misc]simplify: iters left: 4 (46 enodes) 1536750503.427 * * [misc]simplify: iters left: 3 (50 enodes) 1536750503.440 * * [misc]simplify: iters left: 2 (53 enodes) 1536750503.450 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1536750503.450 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536750503.450 * [enter]simplify: Simplifying (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750503.451 * * [misc]simplify: iters left: 6 (14 enodes) 1536750503.454 * * [misc]simplify: iters left: 5 (20 enodes) 1536750503.458 * * [misc]simplify: iters left: 4 (29 enodes) 1536750503.462 * * [misc]simplify: iters left: 3 (30 enodes) 1536750503.467 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750503.467 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536750503.467 * * * * [misc]progress: [ 47 / 76 ] simplifiying candidate # 1536750503.467 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1536750503.468 * * [misc]simplify: iters left: 6 (15 enodes) 1536750503.471 * * [misc]simplify: iters left: 5 (23 enodes) 1536750503.479 * * [misc]simplify: iters left: 4 (34 enodes) 1536750503.489 * * [misc]simplify: iters left: 3 (37 enodes) 1536750503.499 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) 1536750503.499 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))))) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536750503.500 * [enter]simplify: Simplifying (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750503.500 * * [misc]simplify: iters left: 6 (14 enodes) 1536750503.503 * * [misc]simplify: iters left: 5 (20 enodes) 1536750503.508 * * [misc]simplify: iters left: 4 (29 enodes) 1536750503.512 * * [misc]simplify: iters left: 3 (30 enodes) 1536750503.517 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750503.517 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536750503.518 * * * * [misc]progress: [ 48 / 76 ] simplifiying candidate # 1536750503.518 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1) 1536750503.518 * * [misc]simplify: iters left: 6 (14 enodes) 1536750503.522 * * [misc]simplify: iters left: 5 (24 enodes) 1536750503.527 * * [misc]simplify: iters left: 4 (39 enodes) 1536750503.534 * * [misc]simplify: iters left: 3 (54 enodes) 1536750503.543 * * [misc]simplify: iters left: 2 (80 enodes) 1536750503.555 * [exit]simplify: Simplified to (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) 1536750503.555 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k)))) 1536750503.555 * [enter]simplify: Simplifying (/ (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k)) 1536750503.556 * * [misc]simplify: iters left: 6 (13 enodes) 1536750503.560 * * [misc]simplify: iters left: 5 (19 enodes) 1536750503.564 * * [misc]simplify: iters left: 4 (28 enodes) 1536750503.568 * * [misc]simplify: iters left: 3 (30 enodes) 1536750503.573 * [exit]simplify: Simplified to (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt k)) 1536750503.573 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1536750503.573 * * * * [misc]progress: [ 49 / 76 ] simplifiying candidate # 1536750503.573 * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750503.574 * * [misc]simplify: iters left: 6 (15 enodes) 1536750503.577 * * [misc]simplify: iters left: 5 (23 enodes) 1536750503.582 * * [misc]simplify: iters left: 4 (32 enodes) 1536750503.586 * * [misc]simplify: iters left: 3 (34 enodes) 1536750503.592 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750503.592 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536750503.592 * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750503.593 * * [misc]simplify: iters left: 6 (14 enodes) 1536750503.596 * * [misc]simplify: iters left: 5 (20 enodes) 1536750503.599 * * [misc]simplify: iters left: 4 (29 enodes) 1536750503.604 * * [misc]simplify: iters left: 3 (30 enodes) 1536750503.608 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750503.608 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536750503.608 * * * * [misc]progress: [ 50 / 76 ] simplifiying candidate # 1536750503.609 * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750503.609 * * [misc]simplify: iters left: 6 (14 enodes) 1536750503.612 * * [misc]simplify: iters left: 5 (20 enodes) 1536750503.616 * * [misc]simplify: iters left: 4 (29 enodes) 1536750503.620 * * [misc]simplify: iters left: 3 (30 enodes) 1536750503.625 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750503.625 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536750503.625 * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750503.626 * * [misc]simplify: iters left: 6 (14 enodes) 1536750503.630 * * [misc]simplify: iters left: 5 (20 enodes) 1536750503.634 * * [misc]simplify: iters left: 4 (29 enodes) 1536750503.638 * * [misc]simplify: iters left: 3 (30 enodes) 1536750503.643 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750503.643 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536750503.643 * * * * [misc]progress: [ 51 / 76 ] simplifiying candidate # 1536750503.643 * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1) 1536750503.644 * * [misc]simplify: iters left: 6 (13 enodes) 1536750503.646 * * [misc]simplify: iters left: 5 (21 enodes) 1536750503.654 * * [misc]simplify: iters left: 4 (32 enodes) 1536750503.661 * * [misc]simplify: iters left: 3 (33 enodes) 1536750503.665 * [exit]simplify: Simplified to (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) 1536750503.665 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k)))) 1536750503.666 * [enter]simplify: Simplifying (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (sqrt k)) 1536750503.666 * * [misc]simplify: iters left: 6 (13 enodes) 1536750503.669 * * [misc]simplify: iters left: 5 (19 enodes) 1536750503.672 * * [misc]simplify: iters left: 4 (28 enodes) 1536750503.677 * * [misc]simplify: iters left: 3 (30 enodes) 1536750503.682 * [exit]simplify: Simplified to (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt k)) 1536750503.682 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (sqrt k)))) 1536750503.682 * * * * [misc]progress: [ 52 / 76 ] simplifiying candidate # 1536750503.682 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750503.683 * * [misc]simplify: iters left: 6 (6 enodes) 1536750503.684 * * [misc]simplify: iters left: 5 (10 enodes) 1536750503.686 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1536750503.686 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536750503.686 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750503.687 * * [misc]simplify: iters left: 6 (13 enodes) 1536750503.689 * * [misc]simplify: iters left: 5 (19 enodes) 1536750503.693 * * [misc]simplify: iters left: 4 (28 enodes) 1536750503.697 * * [misc]simplify: iters left: 3 (30 enodes) 1536750503.702 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750503.702 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536750503.702 * * * * [misc]progress: [ 53 / 76 ] simplifiying candidate # 1536750503.703 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1536750503.703 * * [misc]simplify: iters left: 4 (5 enodes) 1536750503.704 * * [misc]simplify: iters left: 3 (7 enodes) 1536750503.705 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1536750503.705 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536750503.705 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750503.707 * * [misc]simplify: iters left: 6 (13 enodes) 1536750503.710 * * [misc]simplify: iters left: 5 (19 enodes) 1536750503.715 * * [misc]simplify: iters left: 4 (28 enodes) 1536750503.719 * * [misc]simplify: iters left: 3 (30 enodes) 1536750503.724 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750503.724 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536750503.724 * * * * [misc]progress: [ 54 / 76 ] simplifiying candidate # 1536750503.724 * [enter]simplify: Simplifying (/ 1 1) 1536750503.724 * * [misc]simplify: iters left: 2 (2 enodes) 1536750503.725 * * [misc]simplify: iters left: 1 (4 enodes) 1536750503.725 * [exit]simplify: Simplified to 1 1536750503.725 * [misc]simplify: Simplified (2 1) to (λ (k n) (* 1 (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))) 1536750503.725 * [enter]simplify: Simplifying (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)) 1536750503.726 * * [misc]simplify: iters left: 6 (12 enodes) 1536750503.728 * * [misc]simplify: iters left: 5 (18 enodes) 1536750503.733 * * [misc]simplify: iters left: 4 (27 enodes) 1536750503.737 * * [misc]simplify: iters left: 3 (29 enodes) 1536750503.741 * [exit]simplify: Simplified to (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k)) 1536750503.742 * [misc]simplify: Simplified (2 2) to (λ (k n) (* 1 (/ (pow (* (* PI n) 2) (- 1/2 (/ k 2))) (sqrt k)))) 1536750503.742 * * * * [misc]progress: [ 55 / 76 ] simplifiying candidate # 1536750503.742 * * * * [misc]progress: [ 56 / 76 ] simplifiying candidate # 1536750503.742 * * * * [misc]progress: [ 57 / 76 ] simplifiying candidate # 1536750503.742 * * * * [misc]progress: [ 58 / 76 ] simplifiying candidate # 1536750503.742 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1536750503.742 * * [misc]simplify: iters left: 2 (3 enodes) 1536750503.743 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1536750503.743 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))) 1536750503.743 * * * * [misc]progress: [ 59 / 76 ] simplifiying candidate # 1536750503.743 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1536750503.743 * * [misc]simplify: iters left: 2 (3 enodes) 1536750503.744 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1536750503.744 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))) 1536750503.744 * * * * [misc]progress: [ 60 / 76 ] simplifiying candidate # 1536750503.744 * [enter]simplify: Simplifying (sqrt k) 1536750503.744 * * [misc]simplify: iters left: 1 (2 enodes) 1536750503.744 * [exit]simplify: Simplified to (sqrt k) 1536750503.744 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) 1) (sqrt k))) 1536750503.744 * * * * [misc]progress: [ 61 / 76 ] simplifiying candidate # 1536750503.745 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) 1/2) 1536750503.745 * * [misc]simplify: iters left: 5 (7 enodes) 1536750503.747 * * [misc]simplify: iters left: 4 (12 enodes) 1536750503.750 * * [misc]simplify: iters left: 3 (18 enodes) 1536750503.753 * * [misc]simplify: iters left: 2 (20 enodes) 1536750503.756 * [exit]simplify: Simplified to (sqrt (* (* PI n) 2)) 1536750503.756 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* PI n) 2)) (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2)))))) 1536750503.756 * * * * [misc]progress: [ 62 / 76 ] simplifiying candidate # 1536750503.756 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) 1/2) 1536750503.756 * * [misc]simplify: iters left: 5 (7 enodes) 1536750503.758 * * [misc]simplify: iters left: 4 (12 enodes) 1536750503.760 * * [misc]simplify: iters left: 3 (18 enodes) 1536750503.763 * * [misc]simplify: iters left: 2 (20 enodes) 1536750503.766 * [exit]simplify: Simplified to (sqrt (* (* PI n) 2)) 1536750503.766 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* PI n) 2)) (/ (sqrt k) (pow (* 2 (* n PI)) (- (/ k 2)))))) 1536750503.766 * * * * [misc]progress: [ 63 / 76 ] simplifiying candidate # 1536750503.766 * [enter]simplify: Simplifying (pow 2 (- 1/2 (/ k 2))) 1536750503.767 * * [misc]simplify: iters left: 5 (6 enodes) 1536750503.768 * * [misc]simplify: iters left: 4 (8 enodes) 1536750503.769 * * [misc]simplify: iters left: 3 (11 enodes) 1536750503.771 * [exit]simplify: Simplified to (pow 2 (- 1/2 (/ k 2))) 1536750503.771 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow 2 (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* n PI) (- 1/2 (/ k 2)))))) 1536750503.771 * * * * [misc]progress: [ 64 / 76 ] simplifiying candidate # 1536750503.771 * [enter]simplify: Simplifying (* (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))) 1536750503.772 * * [misc]simplify: iters left: 6 (12 enodes) 1536750503.774 * * [misc]simplify: iters left: 5 (18 enodes) 1536750503.778 * * [misc]simplify: iters left: 4 (27 enodes) 1536750503.788 * * [misc]simplify: iters left: 3 (29 enodes) 1536750503.797 * [exit]simplify: Simplified to (* (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) 1536750503.797 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI n) 2) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))) 1536750503.797 * * * * [misc]progress: [ 65 / 76 ] simplifiying candidate # 1536750503.798 * [enter]simplify: Simplifying (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) 1536750503.799 * * [misc]simplify: iters left: 6 (11 enodes) 1536750503.803 * * [misc]simplify: iters left: 5 (17 enodes) 1536750503.810 * * [misc]simplify: iters left: 4 (26 enodes) 1536750503.817 * * [misc]simplify: iters left: 3 (27 enodes) 1536750503.821 * [exit]simplify: Simplified to (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1536750503.821 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2))))))) 1536750503.821 * * * * [misc]progress: [ 66 / 76 ] simplifiying candidate # 1536750503.821 * * * * [misc]progress: [ 67 / 76 ] simplifiying candidate # 1536750503.821 * [enter]simplify: Simplifying (pow (* 2 (* n PI)) 1/2) 1536750503.821 * * [misc]simplify: iters left: 5 (7 enodes) 1536750503.823 * * [misc]simplify: iters left: 4 (12 enodes) 1536750503.825 * * [misc]simplify: iters left: 3 (18 enodes) 1536750503.828 * * [misc]simplify: iters left: 2 (20 enodes) 1536750503.832 * [exit]simplify: Simplified to (sqrt (* (* PI n) 2)) 1536750503.832 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (sqrt (* (* PI n) 2)) (* (sqrt k) (pow (* 2 (* n PI)) (/ k 2))))) 1536750503.832 * * * * [misc]progress: [ 68 / 76 ] simplifiying candidate # 1536750503.832 * [enter]simplify: Simplifying (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 1536750503.834 * * [misc]simplify: iters left: 6 (37 enodes) 1536750503.848 * * [misc]simplify: iters left: 5 (105 enodes) 1536750503.892 * * [misc]simplify: iters left: 4 (339 enodes) 1536750504.340 * [exit]simplify: Simplified to (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) 1536750504.340 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (+ (+ (* (* (* (* k (pow n 1/2)) (pow (* PI 2) 1/2)) (+ (log n) (log (* PI 2)))) -1/2) (+ (* (* (* k (log n)) (* k (log n))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (pow (* PI 2) 1/2) (pow n 1/2)))) (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (* 1/8 (pow n 1/2)) (pow (* PI 2) 1/2))) (* (* (* (log n) (pow n 1/2)) (pow (* PI 2) 1/2)) (* (log (* PI 2)) 1/4))))) (sqrt k))) 1536750504.340 * * * * [misc]progress: [ 69 / 76 ] simplifiying candidate # 1536750504.340 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 1536750504.341 * * [misc]simplify: iters left: 6 (15 enodes) 1536750504.346 * * [misc]simplify: iters left: 5 (33 enodes) 1536750504.355 * * [misc]simplify: iters left: 4 (64 enodes) 1536750504.376 * * [misc]simplify: iters left: 3 (171 enodes) 1536750504.584 * [exit]simplify: Simplified to (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) 1536750504.584 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (pow (* 2 PI) (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (sqrt k))) 1536750504.584 * * * * [misc]progress: [ 70 / 76 ] simplifiying candidate # 1536750504.584 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 1536750504.585 * * [misc]simplify: iters left: 6 (15 enodes) 1536750504.590 * * [misc]simplify: iters left: 5 (30 enodes) 1536750504.598 * * [misc]simplify: iters left: 4 (65 enodes) 1536750504.632 * * [misc]simplify: iters left: 3 (200 enodes) 1536750504.920 * [exit]simplify: Simplified to (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) 1536750504.920 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (pow (exp (- 1/2 (* 1/2 k))) (- (log (* -2 PI)) (log (/ -1 n)))) (sqrt k))) 1536750504.920 * * * * [misc]progress: [ 71 / 76 ] simplifiying candidate # 1536750504.920 * [enter]simplify: Simplifying (* n PI) 1536750504.921 * * [misc]simplify: iters left: 2 (3 enodes) 1536750504.922 * * [misc]simplify: iters left: 1 (4 enodes) 1536750504.923 * [exit]simplify: Simplified to (* n PI) 1536750504.923 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) 1536750504.924 * * * * [misc]progress: [ 72 / 76 ] simplifiying candidate # 1536750504.924 * [enter]simplify: Simplifying (* n PI) 1536750504.924 * * [misc]simplify: iters left: 2 (3 enodes) 1536750504.925 * * [misc]simplify: iters left: 1 (4 enodes) 1536750504.927 * [exit]simplify: Simplified to (* n PI) 1536750504.927 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) 1536750504.927 * * * * [misc]progress: [ 73 / 76 ] simplifiying candidate # 1536750504.927 * [enter]simplify: Simplifying (* n PI) 1536750504.927 * * [misc]simplify: iters left: 2 (3 enodes) 1536750504.928 * * [misc]simplify: iters left: 1 (4 enodes) 1536750504.930 * [exit]simplify: Simplified to (* n PI) 1536750504.930 * [misc]simplify: Simplified (2 1 1 2) to (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k))) 1536750504.930 * * * * [misc]progress: [ 74 / 76 ] simplifiying candidate # 1536750504.930 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 1536750504.930 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536750504.930 * * * * [misc]progress: [ 75 / 76 ] simplifiying candidate # 1536750504.930 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 1536750504.930 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536750504.931 * * * * [misc]progress: [ 76 / 76 ] simplifiying candidate # 1536750504.931 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 1536750504.931 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536750504.931 * * * [misc]progress: adding candidates to table 1536750506.461 * * [misc]progress: iteration 3 / 4 1536750506.461 * * * [misc]progress: picking best candidate 1536750506.542 * * * * [misc]pick: Picked # 1536750506.542 * * * [misc]progress: localizing error 1536750506.590 * * * [misc]progress: generating rewritten candidates 1536750506.590 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2) 1536750506.664 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2 2 1) 1536750506.675 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2 1 1) 1536750506.676 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2) 1536750506.704 * * * [misc]progress: generating series expansions 1536750506.704 * * * * [misc]progress: [ 1 / 4 ] generating series at (2) 1536750506.704 * [misc]backup-simplify: Simplify (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) into (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 1536750506.704 * [misc]approximate: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in (k n) around 0 1536750506.704 * [misc]taylor: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 1536750506.705 * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in n 1536750506.705 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n 1536750506.705 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n 1536750506.705 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n 1536750506.705 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750506.705 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.705 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.705 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750506.705 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.705 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.705 * [misc]taylor: Taking taylor expansion of k in n 1536750506.705 * [misc]backup-simplify: Simplify k into k 1536750506.705 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536750506.705 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750506.705 * [misc]taylor: Taking taylor expansion of n in n 1536750506.705 * [misc]backup-simplify: Simplify 0 into 0 1536750506.705 * [misc]backup-simplify: Simplify 1 into 1 1536750506.705 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.705 * [misc]backup-simplify: Simplify PI into PI 1536750506.705 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750506.706 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750506.706 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750506.706 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750506.706 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750506.706 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750506.706 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750506.707 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) 1536750506.707 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 1536750506.707 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in n 1536750506.707 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in n 1536750506.707 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in n 1536750506.707 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750506.707 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.707 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.707 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750506.707 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.707 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.707 * [misc]taylor: Taking taylor expansion of k in n 1536750506.707 * [misc]backup-simplify: Simplify k into k 1536750506.707 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750506.707 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.707 * [misc]backup-simplify: Simplify 2 into 2 1536750506.707 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750506.707 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750506.707 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750506.707 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750506.708 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log 2)) into (* (log 2) (- 1/2 (* 1/2 k))) 1536750506.708 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 k)))) into (exp (* (log 2) (- 1/2 (* 1/2 k)))) 1536750506.708 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536750506.708 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750506.708 * [misc]taylor: Taking taylor expansion of k in n 1536750506.708 * [misc]backup-simplify: Simplify k into k 1536750506.708 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750506.708 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536750506.708 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750506.708 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536750506.708 * [misc]taylor: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1536750506.708 * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in k 1536750506.708 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k 1536750506.708 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k 1536750506.708 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k 1536750506.708 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750506.708 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.708 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.708 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750506.708 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.708 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.708 * [misc]taylor: Taking taylor expansion of k in k 1536750506.708 * [misc]backup-simplify: Simplify 0 into 0 1536750506.708 * [misc]backup-simplify: Simplify 1 into 1 1536750506.708 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in k 1536750506.708 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536750506.708 * [misc]taylor: Taking taylor expansion of n in k 1536750506.708 * [misc]backup-simplify: Simplify n into n 1536750506.708 * [misc]taylor: Taking taylor expansion of PI in k 1536750506.708 * [misc]backup-simplify: Simplify PI into PI 1536750506.708 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536750506.708 * [misc]backup-simplify: Simplify (log (* n PI)) into (log (* n PI)) 1536750506.709 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750506.709 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.709 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750506.709 * [misc]backup-simplify: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI))) 1536750506.709 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2) 1536750506.709 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k 1536750506.709 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k 1536750506.709 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k 1536750506.709 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750506.709 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.709 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.709 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750506.709 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.709 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.709 * [misc]taylor: Taking taylor expansion of k in k 1536750506.709 * [misc]backup-simplify: Simplify 0 into 0 1536750506.709 * [misc]backup-simplify: Simplify 1 into 1 1536750506.709 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536750506.709 * [misc]taylor: Taking taylor expansion of 2 in k 1536750506.709 * [misc]backup-simplify: Simplify 2 into 2 1536750506.709 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750506.709 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750506.710 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.710 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750506.710 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536750506.710 * [misc]backup-simplify: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 1536750506.710 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536750506.710 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750506.710 * [misc]taylor: Taking taylor expansion of k in k 1536750506.710 * [misc]backup-simplify: Simplify 0 into 0 1536750506.710 * [misc]backup-simplify: Simplify 1 into 1 1536750506.710 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750506.710 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750506.711 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750506.711 * [misc]taylor: Taking taylor expansion of (* (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1536750506.711 * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) in k 1536750506.711 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k 1536750506.711 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k 1536750506.711 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k 1536750506.711 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750506.711 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.711 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.711 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750506.711 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.711 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.711 * [misc]taylor: Taking taylor expansion of k in k 1536750506.711 * [misc]backup-simplify: Simplify 0 into 0 1536750506.711 * [misc]backup-simplify: Simplify 1 into 1 1536750506.711 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in k 1536750506.711 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536750506.711 * [misc]taylor: Taking taylor expansion of n in k 1536750506.711 * [misc]backup-simplify: Simplify n into n 1536750506.711 * [misc]taylor: Taking taylor expansion of PI in k 1536750506.711 * [misc]backup-simplify: Simplify PI into PI 1536750506.711 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536750506.711 * [misc]backup-simplify: Simplify (log (* n PI)) into (log (* n PI)) 1536750506.711 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750506.711 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.712 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750506.712 * [misc]backup-simplify: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI))) 1536750506.712 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2) 1536750506.712 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k 1536750506.712 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k 1536750506.712 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k 1536750506.712 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750506.712 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.712 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.712 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750506.712 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.712 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.712 * [misc]taylor: Taking taylor expansion of k in k 1536750506.712 * [misc]backup-simplify: Simplify 0 into 0 1536750506.712 * [misc]backup-simplify: Simplify 1 into 1 1536750506.712 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536750506.712 * [misc]taylor: Taking taylor expansion of 2 in k 1536750506.712 * [misc]backup-simplify: Simplify 2 into 2 1536750506.712 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750506.712 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750506.712 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.712 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750506.713 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536750506.713 * [misc]backup-simplify: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 1536750506.713 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536750506.713 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750506.713 * [misc]taylor: Taking taylor expansion of k in k 1536750506.713 * [misc]backup-simplify: Simplify 0 into 0 1536750506.713 * [misc]backup-simplify: Simplify 1 into 1 1536750506.713 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750506.713 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750506.713 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750506.714 * [misc]backup-simplify: Simplify (* (pow (* n PI) 1/2) (pow 2 1/2)) into (sqrt (* n (* PI 2))) 1536750506.714 * [misc]backup-simplify: Simplify (* (sqrt (* n (* PI 2))) 0) into 0 1536750506.714 * [misc]taylor: Taking taylor expansion of 0 in n 1536750506.714 * [misc]backup-simplify: Simplify 0 into 0 1536750506.714 * [misc]backup-simplify: Simplify 0 into 0 1536750506.716 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536750506.716 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536750506.716 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750506.716 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750506.716 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log 2))) into (- (* 1/2 (log 2))) 1536750506.718 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 1) 1)))) into (* -1/2 (* (log 2) (sqrt 2))) 1536750506.718 * [misc]backup-simplify: Simplify (+ (* n 0) (* 0 PI)) into 0 1536750506.719 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* n PI) 1)))) 1) into 0 1536750506.719 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536750506.719 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750506.720 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750506.720 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log (* n PI)))) into (- (* 1/2 (log (* n PI)))) 1536750506.720 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 1) 1)))) into (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) 1536750506.721 * [misc]backup-simplify: Simplify (+ (* (pow (* n PI) 1/2) (* -1/2 (* (log 2) (sqrt 2)))) (* (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) (pow 2 1/2))) into (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) 1536750506.722 * [misc]backup-simplify: Simplify (+ (* (sqrt (* n (* PI 2))) +nan.0) (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1536750506.722 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1536750506.722 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1536750506.722 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750506.722 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750506.722 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1536750506.722 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750506.722 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.722 * [misc]backup-simplify: Simplify 2 into 2 1536750506.723 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750506.723 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750506.723 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750506.723 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750506.723 * [misc]taylor: Taking taylor expansion of n in n 1536750506.723 * [misc]backup-simplify: Simplify 0 into 0 1536750506.723 * [misc]backup-simplify: Simplify 1 into 1 1536750506.723 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.723 * [misc]backup-simplify: Simplify PI into PI 1536750506.723 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750506.723 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750506.724 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750506.724 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750506.724 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536750506.724 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750506.724 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.724 * [misc]backup-simplify: Simplify 0 into 0 1536750506.724 * [misc]backup-simplify: Simplify 0 into 0 1536750506.724 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536750506.725 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750506.728 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1536750506.728 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536750506.728 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.728 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750506.728 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log 2)))) into 0 1536750506.736 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log 2) 2) (sqrt 2))) 1536750506.738 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1536750506.740 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* n PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* n PI) 1)))) 2) into 0 1536750506.740 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536750506.740 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.740 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750506.741 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* n PI))))) into 0 1536750506.742 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI)))) 1536750506.747 * [misc]backup-simplify: Simplify (+ (* (pow (* n PI) 1/2) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI)))) (pow 2 1/2)))) into (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))))) 1536750506.754 * [misc]backup-simplify: Simplify (+ (* (sqrt (* n (* PI 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) +nan.0) (* (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) 1536750506.754 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n 1536750506.754 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n 1536750506.754 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n 1536750506.754 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750506.754 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750506.755 * [misc]taylor: Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n 1536750506.755 * [misc]taylor: Taking taylor expansion of (* (log 2) (sqrt 2)) in n 1536750506.755 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750506.755 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.755 * [misc]backup-simplify: Simplify 2 into 2 1536750506.755 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750506.755 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750506.755 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.755 * [misc]backup-simplify: Simplify 2 into 2 1536750506.755 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750506.755 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750506.755 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750506.755 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750506.755 * [misc]taylor: Taking taylor expansion of n in n 1536750506.755 * [misc]backup-simplify: Simplify 0 into 0 1536750506.755 * [misc]backup-simplify: Simplify 1 into 1 1536750506.755 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.755 * [misc]backup-simplify: Simplify PI into PI 1536750506.756 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750506.756 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750506.756 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750506.757 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750506.757 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 1536750506.757 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 1536750506.757 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) in n 1536750506.757 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750506.757 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750506.757 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))) in n 1536750506.757 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n 1536750506.757 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750506.757 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.757 * [misc]backup-simplify: Simplify 2 into 2 1536750506.757 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750506.757 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750506.757 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536750506.758 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750506.758 * [misc]taylor: Taking taylor expansion of n in n 1536750506.758 * [misc]backup-simplify: Simplify 0 into 0 1536750506.758 * [misc]backup-simplify: Simplify 1 into 1 1536750506.758 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.758 * [misc]backup-simplify: Simplify PI into PI 1536750506.758 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750506.758 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750506.759 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750506.759 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750506.759 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750506.759 * [misc]taylor: Taking taylor expansion of n in n 1536750506.759 * [misc]backup-simplify: Simplify 0 into 0 1536750506.759 * [misc]backup-simplify: Simplify 1 into 1 1536750506.759 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.759 * [misc]backup-simplify: Simplify PI into PI 1536750506.759 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750506.760 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750506.760 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750506.760 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750506.760 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1536750506.760 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1536750506.760 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750506.760 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750506.760 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1536750506.761 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750506.761 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.761 * [misc]backup-simplify: Simplify 2 into 2 1536750506.761 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750506.761 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750506.761 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750506.761 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750506.761 * [misc]taylor: Taking taylor expansion of n in n 1536750506.761 * [misc]backup-simplify: Simplify 0 into 0 1536750506.761 * [misc]backup-simplify: Simplify 1 into 1 1536750506.761 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.761 * [misc]backup-simplify: Simplify PI into PI 1536750506.761 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750506.762 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750506.762 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750506.762 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750506.763 * [misc]backup-simplify: Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2)) 1536750506.763 * [misc]backup-simplify: Simplify (* (* (log 2) (sqrt 2)) 0) into 0 1536750506.763 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750506.764 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750506.764 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n))) 1536750506.765 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log PI) (log n))) 0) into 0 1536750506.765 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750506.765 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536750506.765 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750506.765 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.765 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750506.766 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.766 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750506.766 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.766 * [misc]backup-simplify: Simplify 0 into 0 1536750506.767 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536750506.769 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536750506.770 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536750506.771 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536750506.771 * [misc]backup-simplify: Simplify 0 into 0 1536750506.771 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750506.772 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750506.779 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1536750506.779 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536750506.779 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.779 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750506.780 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log 2))))) into 0 1536750506.786 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 3) 6)) (* (/ (pow (- (* 1/2 (log 2))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log 2) 3) (sqrt 2))) 1536750506.787 * [misc]backup-simplify: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750506.790 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* n PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* n PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* n PI) 1)))) 6) into 0 1536750506.790 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536750506.790 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.791 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750506.791 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* n PI)))))) into 0 1536750506.794 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log (* n PI)))) (+ (* (/ (pow (- (* 1/2 (log (* n PI)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* n PI)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log (* n PI)) 3) (sqrt (* n PI)))) 1536750506.805 * [misc]backup-simplify: Simplify (+ (* (pow (* n PI) 1/2) (* -1/48 (* (pow (log 2) 3) (sqrt 2)))) (+ (* (* -1/2 (* (log (* n PI)) (sqrt (* n PI)))) (* 1/8 (* (pow (log 2) 2) (sqrt 2)))) (+ (* (* 1/8 (* (pow (log (* n PI)) 2) (sqrt (* n PI)))) (* -1/2 (* (log 2) (sqrt 2)))) (* (* -1/48 (* (pow (log (* n PI)) 3) (sqrt (* n PI)))) (pow 2 1/2))))) into (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log (* n PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* n PI)) 3)) (sqrt (* n PI)))))))) 1536750506.827 * [misc]backup-simplify: Simplify (+ (* (sqrt (* n (* PI 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (* 1/2 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) +nan.0) (+ (* (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/8 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))))) +nan.0) (* (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log (* n PI)) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (* 1/48 (* (* (sqrt 2) (pow (log (* n PI)) 3)) (sqrt (* n PI)))))))) 0)))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))))))))) 1536750506.827 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))))))))) in n 1536750506.827 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))))))))) in n 1536750506.827 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n 1536750506.827 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750506.827 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750506.827 * [misc]taylor: Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n 1536750506.827 * [misc]taylor: Taking taylor expansion of (* (log 2) (sqrt 2)) in n 1536750506.827 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750506.827 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.827 * [misc]backup-simplify: Simplify 2 into 2 1536750506.827 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750506.827 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750506.827 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.827 * [misc]backup-simplify: Simplify 2 into 2 1536750506.828 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750506.828 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750506.828 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750506.828 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750506.828 * [misc]taylor: Taking taylor expansion of n in n 1536750506.828 * [misc]backup-simplify: Simplify 0 into 0 1536750506.828 * [misc]backup-simplify: Simplify 1 into 1 1536750506.828 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.828 * [misc]backup-simplify: Simplify PI into PI 1536750506.828 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750506.828 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750506.829 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750506.829 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750506.829 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))))))) in n 1536750506.829 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))))))) in n 1536750506.829 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) in n 1536750506.829 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750506.829 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750506.829 * [misc]taylor: Taking taylor expansion of (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI))) in n 1536750506.829 * [misc]taylor: Taking taylor expansion of (* (pow (log 2) 2) (sqrt 2)) in n 1536750506.829 * [misc]taylor: Taking taylor expansion of (pow (log 2) 2) in n 1536750506.829 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750506.829 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.829 * [misc]backup-simplify: Simplify 2 into 2 1536750506.829 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750506.829 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750506.829 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.829 * [misc]backup-simplify: Simplify 2 into 2 1536750506.829 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750506.830 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750506.830 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750506.830 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750506.830 * [misc]taylor: Taking taylor expansion of n in n 1536750506.830 * [misc]backup-simplify: Simplify 0 into 0 1536750506.830 * [misc]backup-simplify: Simplify 1 into 1 1536750506.830 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.830 * [misc]backup-simplify: Simplify PI into PI 1536750506.830 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750506.830 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750506.830 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750506.831 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750506.831 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))))) in n 1536750506.831 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))))) in n 1536750506.831 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI)))) in n 1536750506.831 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750506.831 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750506.831 * [misc]taylor: Taking taylor expansion of (* (* (log 2) (* (sqrt 2) (log (* n PI)))) (sqrt (* n PI))) in n 1536750506.831 * [misc]taylor: Taking taylor expansion of (* (log 2) (* (sqrt 2) (log (* n PI)))) in n 1536750506.831 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750506.831 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.831 * [misc]backup-simplify: Simplify 2 into 2 1536750506.831 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750506.831 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n 1536750506.831 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750506.831 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.831 * [misc]backup-simplify: Simplify 2 into 2 1536750506.831 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750506.831 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750506.831 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536750506.831 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750506.831 * [misc]taylor: Taking taylor expansion of n in n 1536750506.831 * [misc]backup-simplify: Simplify 0 into 0 1536750506.831 * [misc]backup-simplify: Simplify 1 into 1 1536750506.831 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.831 * [misc]backup-simplify: Simplify PI into PI 1536750506.832 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750506.832 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750506.832 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750506.832 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750506.832 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750506.832 * [misc]taylor: Taking taylor expansion of n in n 1536750506.832 * [misc]backup-simplify: Simplify 0 into 0 1536750506.832 * [misc]backup-simplify: Simplify 1 into 1 1536750506.832 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.832 * [misc]backup-simplify: Simplify PI into PI 1536750506.833 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750506.833 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750506.833 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750506.833 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750506.833 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))))) in n 1536750506.833 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))))) in n 1536750506.833 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI)))) in n 1536750506.833 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750506.834 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750506.834 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* n PI)) 2)) (sqrt (* n PI))) in n 1536750506.834 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log (* n PI)) 2)) in n 1536750506.834 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750506.834 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.834 * [misc]backup-simplify: Simplify 2 into 2 1536750506.834 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750506.834 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750506.834 * [misc]taylor: Taking taylor expansion of (pow (log (* n PI)) 2) in n 1536750506.834 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536750506.834 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750506.834 * [misc]taylor: Taking taylor expansion of n in n 1536750506.834 * [misc]backup-simplify: Simplify 0 into 0 1536750506.834 * [misc]backup-simplify: Simplify 1 into 1 1536750506.834 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.834 * [misc]backup-simplify: Simplify PI into PI 1536750506.834 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750506.835 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750506.835 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750506.835 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750506.835 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750506.835 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750506.835 * [misc]taylor: Taking taylor expansion of n in n 1536750506.835 * [misc]backup-simplify: Simplify 0 into 0 1536750506.835 * [misc]backup-simplify: Simplify 1 into 1 1536750506.835 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.835 * [misc]backup-simplify: Simplify PI into PI 1536750506.835 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750506.836 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750506.836 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750506.836 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750506.836 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))))) in n 1536750506.836 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))))) in n 1536750506.836 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1536750506.836 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750506.836 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750506.836 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1536750506.836 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750506.836 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.836 * [misc]backup-simplify: Simplify 2 into 2 1536750506.837 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750506.837 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750506.837 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750506.837 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750506.837 * [misc]taylor: Taking taylor expansion of n in n 1536750506.837 * [misc]backup-simplify: Simplify 0 into 0 1536750506.837 * [misc]backup-simplify: Simplify 1 into 1 1536750506.837 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.837 * [misc]backup-simplify: Simplify PI into PI 1536750506.837 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750506.837 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750506.838 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750506.838 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750506.838 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))))) in n 1536750506.838 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI)))) in n 1536750506.838 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750506.838 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750506.838 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log (* n PI))) (sqrt (* n PI))) in n 1536750506.838 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log (* n PI))) in n 1536750506.838 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750506.838 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.838 * [misc]backup-simplify: Simplify 2 into 2 1536750506.838 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750506.838 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750506.838 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536750506.838 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750506.838 * [misc]taylor: Taking taylor expansion of n in n 1536750506.838 * [misc]backup-simplify: Simplify 0 into 0 1536750506.838 * [misc]backup-simplify: Simplify 1 into 1 1536750506.838 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.838 * [misc]backup-simplify: Simplify PI into PI 1536750506.839 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750506.839 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750506.839 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750506.839 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750506.839 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750506.839 * [misc]taylor: Taking taylor expansion of n in n 1536750506.839 * [misc]backup-simplify: Simplify 0 into 0 1536750506.839 * [misc]backup-simplify: Simplify 1 into 1 1536750506.839 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.839 * [misc]backup-simplify: Simplify PI into PI 1536750506.839 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750506.840 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750506.840 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750506.840 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750506.841 * [misc]backup-simplify: Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2)) 1536750506.841 * [misc]backup-simplify: Simplify (* (* (log 2) (sqrt 2)) 0) into 0 1536750506.841 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750506.841 * [misc]backup-simplify: Simplify (* (log 2) (log 2)) into (pow (log 2) 2) 1536750506.842 * [misc]backup-simplify: Simplify (* (pow (log 2) 2) (sqrt 2)) into (* (pow (log 2) 2) (sqrt 2)) 1536750506.843 * [misc]backup-simplify: Simplify (* (* (pow (log 2) 2) (sqrt 2)) 0) into 0 1536750506.843 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750506.844 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750506.844 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n))) 1536750506.845 * [misc]backup-simplify: Simplify (* (log 2) (* (sqrt 2) (+ (log PI) (log n)))) into (* (log 2) (* (sqrt 2) (+ (log PI) (log n)))) 1536750506.846 * [misc]backup-simplify: Simplify (* (* (log 2) (* (sqrt 2) (+ (log PI) (log n)))) 0) into 0 1536750506.846 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750506.846 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750506.847 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750506.860 * [misc]backup-simplify: Simplify (* (+ (log PI) (log n)) (+ (log PI) (log n))) into (pow (+ (log PI) (log n)) 2) 1536750506.867 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (+ (log PI) (log n)) 2)) into (* (sqrt 2) (pow (+ (log PI) (log n)) 2)) 1536750506.868 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (+ (log PI) (log n)) 2)) 0) into 0 1536750506.869 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750506.869 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536750506.869 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750506.869 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750506.870 * [misc]backup-simplify: Simplify (* (sqrt 2) (+ (log PI) (log n))) into (* (sqrt 2) (+ (log PI) (log n))) 1536750506.870 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (+ (log PI) (log n))) 0) into 0 1536750506.871 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750506.871 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.871 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750506.871 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.871 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750506.871 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.871 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750506.872 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.872 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750506.872 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.872 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750506.872 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.872 * [misc]backup-simplify: Simplify 0 into 0 1536750506.875 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536750506.875 * [misc]backup-simplify: Simplify (+ (* (log 2) 0) (* 0 (sqrt 2))) into 0 1536750506.876 * [misc]backup-simplify: Simplify (+ (* (* (log 2) (sqrt 2)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) 1536750506.879 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) 1536750506.880 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536750506.882 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750506.882 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750506.883 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log PI) (log n)))) into 0 1536750506.884 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (+ (log PI) (log n))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))))) 1536750506.886 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))))) 1536750506.887 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536750506.890 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536750506.891 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536750506.895 * [misc]backup-simplify: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1536750506.900 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1536750506.906 * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1536750506.914 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1536750506.922 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1536750506.923 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536750506.926 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1536750506.927 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1536750506.930 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536750506.935 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536750506.938 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536750506.939 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536750506.951 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 1536750506.952 * [misc]backup-simplify: Simplify (* (pow 2 (- 1/2 (/ (/ 1 k) 2))) (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) into (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 1536750506.952 * [misc]approximate: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in (k n) around 0 1536750506.952 * [misc]taylor: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 1536750506.952 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750506.952 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750506.952 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in n 1536750506.952 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in n 1536750506.952 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750506.952 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.952 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.952 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750506.952 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.952 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.952 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750506.952 * [misc]taylor: Taking taylor expansion of k in n 1536750506.952 * [misc]backup-simplify: Simplify k into k 1536750506.953 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750506.953 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750506.953 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.953 * [misc]backup-simplify: Simplify 2 into 2 1536750506.953 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750506.953 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750506.953 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750506.953 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750506.953 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536750506.954 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536750506.954 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750506.954 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536750506.954 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536750506.954 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750506.954 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.954 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.954 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750506.954 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.954 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.954 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750506.954 * [misc]taylor: Taking taylor expansion of k in n 1536750506.954 * [misc]backup-simplify: Simplify k into k 1536750506.955 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750506.955 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536750506.955 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750506.955 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.955 * [misc]backup-simplify: Simplify PI into PI 1536750506.955 * [misc]taylor: Taking taylor expansion of n in n 1536750506.955 * [misc]backup-simplify: Simplify 0 into 0 1536750506.955 * [misc]backup-simplify: Simplify 1 into 1 1536750506.955 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750506.956 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750506.956 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750506.956 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750506.956 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750506.956 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536750506.957 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536750506.957 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536750506.957 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536750506.957 * [misc]taylor: Taking taylor expansion of k in n 1536750506.957 * [misc]backup-simplify: Simplify k into k 1536750506.957 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536750506.958 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536750506.958 * [misc]taylor: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1536750506.958 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536750506.958 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750506.958 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k 1536750506.958 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k 1536750506.958 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750506.958 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.958 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.958 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750506.958 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.958 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.958 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750506.958 * [misc]taylor: Taking taylor expansion of k in k 1536750506.958 * [misc]backup-simplify: Simplify 0 into 0 1536750506.958 * [misc]backup-simplify: Simplify 1 into 1 1536750506.958 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750506.958 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536750506.958 * [misc]taylor: Taking taylor expansion of 2 in k 1536750506.958 * [misc]backup-simplify: Simplify 2 into 2 1536750506.959 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750506.959 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750506.959 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750506.959 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750506.959 * [misc]backup-simplify: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) 1536750506.960 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536750506.960 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750506.960 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k 1536750506.960 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k 1536750506.960 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750506.960 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.960 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.960 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750506.960 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.960 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.960 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750506.960 * [misc]taylor: Taking taylor expansion of k in k 1536750506.960 * [misc]backup-simplify: Simplify 0 into 0 1536750506.960 * [misc]backup-simplify: Simplify 1 into 1 1536750506.960 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750506.960 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in k 1536750506.960 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750506.960 * [misc]taylor: Taking taylor expansion of PI in k 1536750506.960 * [misc]backup-simplify: Simplify PI into PI 1536750506.960 * [misc]taylor: Taking taylor expansion of n in k 1536750506.960 * [misc]backup-simplify: Simplify n into n 1536750506.961 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750506.961 * [misc]backup-simplify: Simplify (log (/ PI n)) into (log (/ PI n)) 1536750506.961 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750506.961 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750506.961 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750506.961 * [misc]backup-simplify: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n))) 1536750506.962 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) 1536750506.962 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536750506.962 * [misc]taylor: Taking taylor expansion of k in k 1536750506.962 * [misc]backup-simplify: Simplify 0 into 0 1536750506.962 * [misc]backup-simplify: Simplify 1 into 1 1536750506.962 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750506.962 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750506.962 * [misc]taylor: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1536750506.962 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536750506.962 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750506.963 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k 1536750506.963 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k 1536750506.963 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750506.963 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.963 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.963 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750506.963 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.963 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.963 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750506.963 * [misc]taylor: Taking taylor expansion of k in k 1536750506.963 * [misc]backup-simplify: Simplify 0 into 0 1536750506.963 * [misc]backup-simplify: Simplify 1 into 1 1536750506.963 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750506.963 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536750506.963 * [misc]taylor: Taking taylor expansion of 2 in k 1536750506.963 * [misc]backup-simplify: Simplify 2 into 2 1536750506.963 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750506.963 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750506.964 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750506.964 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750506.964 * [misc]backup-simplify: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) 1536750506.964 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536750506.964 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750506.964 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k 1536750506.964 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k 1536750506.965 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750506.965 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.965 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.965 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750506.965 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750506.965 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.965 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750506.965 * [misc]taylor: Taking taylor expansion of k in k 1536750506.965 * [misc]backup-simplify: Simplify 0 into 0 1536750506.965 * [misc]backup-simplify: Simplify 1 into 1 1536750506.965 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750506.965 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in k 1536750506.965 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750506.965 * [misc]taylor: Taking taylor expansion of PI in k 1536750506.965 * [misc]backup-simplify: Simplify PI into PI 1536750506.965 * [misc]taylor: Taking taylor expansion of n in k 1536750506.965 * [misc]backup-simplify: Simplify n into n 1536750506.965 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750506.965 * [misc]backup-simplify: Simplify (log (/ PI n)) into (log (/ PI n)) 1536750506.966 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750506.966 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750506.966 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750506.966 * [misc]backup-simplify: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n))) 1536750506.966 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) 1536750506.966 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536750506.966 * [misc]taylor: Taking taylor expansion of k in k 1536750506.966 * [misc]backup-simplify: Simplify 0 into 0 1536750506.966 * [misc]backup-simplify: Simplify 1 into 1 1536750506.967 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750506.967 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750506.968 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) 1536750506.968 * [misc]backup-simplify: Simplify (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1536750506.968 * [misc]taylor: Taking taylor expansion of 0 in n 1536750506.968 * [misc]backup-simplify: Simplify 0 into 0 1536750506.968 * [misc]backup-simplify: Simplify 0 into 0 1536750506.969 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) into 0 1536750506.970 * [misc]backup-simplify: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) 1536750506.970 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1536750506.970 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1536750506.970 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750506.970 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750506.970 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750506.970 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750506.970 * [misc]taylor: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750506.970 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750506.970 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.970 * [misc]backup-simplify: Simplify 2 into 2 1536750506.970 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750506.970 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750506.970 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.970 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.970 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750506.970 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.970 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.970 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750506.970 * [misc]taylor: Taking taylor expansion of k in n 1536750506.970 * [misc]backup-simplify: Simplify k into k 1536750506.970 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750506.971 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750506.971 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750506.971 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750506.971 * [misc]backup-simplify: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536750506.971 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536750506.971 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750506.971 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536750506.971 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536750506.972 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750506.972 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.972 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.972 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750506.972 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.972 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.972 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750506.972 * [misc]taylor: Taking taylor expansion of k in n 1536750506.972 * [misc]backup-simplify: Simplify k into k 1536750506.972 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750506.972 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536750506.972 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750506.972 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.972 * [misc]backup-simplify: Simplify PI into PI 1536750506.972 * [misc]taylor: Taking taylor expansion of n in n 1536750506.972 * [misc]backup-simplify: Simplify 0 into 0 1536750506.972 * [misc]backup-simplify: Simplify 1 into 1 1536750506.972 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750506.973 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750506.973 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750506.973 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750506.973 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750506.973 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536750506.974 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536750506.974 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536750506.975 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1536750506.976 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536750506.977 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536750506.978 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536750506.978 * [misc]backup-simplify: Simplify 0 into 0 1536750506.979 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750506.980 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 1536750506.981 * [misc]backup-simplify: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) 1536750506.981 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1536750506.981 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1536750506.981 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750506.981 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750506.981 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750506.981 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750506.981 * [misc]taylor: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750506.981 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750506.981 * [misc]taylor: Taking taylor expansion of 2 in n 1536750506.981 * [misc]backup-simplify: Simplify 2 into 2 1536750506.981 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750506.981 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750506.981 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.981 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.981 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750506.981 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.981 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.981 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750506.981 * [misc]taylor: Taking taylor expansion of k in n 1536750506.981 * [misc]backup-simplify: Simplify k into k 1536750506.982 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750506.982 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750506.982 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750506.982 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750506.982 * [misc]backup-simplify: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536750506.982 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536750506.983 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750506.983 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536750506.983 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536750506.983 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750506.983 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.983 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.983 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750506.983 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750506.983 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750506.983 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750506.983 * [misc]taylor: Taking taylor expansion of k in n 1536750506.983 * [misc]backup-simplify: Simplify k into k 1536750506.983 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750506.983 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536750506.983 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750506.983 * [misc]taylor: Taking taylor expansion of PI in n 1536750506.983 * [misc]backup-simplify: Simplify PI into PI 1536750506.983 * [misc]taylor: Taking taylor expansion of n in n 1536750506.983 * [misc]backup-simplify: Simplify 0 into 0 1536750506.983 * [misc]backup-simplify: Simplify 1 into 1 1536750506.983 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750506.984 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750506.984 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750506.984 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750506.984 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750506.985 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536750506.985 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536750506.986 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536750506.986 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1536750506.987 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536750506.988 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536750506.989 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536750506.990 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750506.993 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750506.993 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750506.993 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750506.993 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.993 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750506.994 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536750506.994 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0 1536750506.996 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750506.996 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750506.996 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750506.996 * [misc]backup-simplify: Simplify (- 0) into 0 1536750506.996 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750506.998 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536750506.999 * [misc]backup-simplify: Simplify (+ (* (log 2) 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0 1536750507.000 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750507.001 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 1536750507.002 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1536750507.002 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.002 * [misc]backup-simplify: Simplify 0 into 0 1536750507.002 * [misc]backup-simplify: Simplify 0 into 0 1536750507.003 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750507.004 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1536750507.005 * [misc]backup-simplify: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) 1536750507.005 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1536750507.005 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1536750507.005 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750507.005 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750507.005 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750507.005 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750507.005 * [misc]taylor: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750507.005 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750507.005 * [misc]taylor: Taking taylor expansion of 2 in n 1536750507.005 * [misc]backup-simplify: Simplify 2 into 2 1536750507.005 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750507.005 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750507.005 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.005 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.005 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.005 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.005 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.005 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.005 * [misc]taylor: Taking taylor expansion of k in n 1536750507.005 * [misc]backup-simplify: Simplify k into k 1536750507.005 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.005 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.006 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750507.006 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750507.006 * [misc]backup-simplify: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536750507.006 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536750507.006 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750507.006 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536750507.006 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536750507.006 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750507.006 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.006 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.006 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.006 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.006 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.006 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.006 * [misc]taylor: Taking taylor expansion of k in n 1536750507.006 * [misc]backup-simplify: Simplify k into k 1536750507.007 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.007 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536750507.007 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.007 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.007 * [misc]backup-simplify: Simplify PI into PI 1536750507.007 * [misc]taylor: Taking taylor expansion of n in n 1536750507.007 * [misc]backup-simplify: Simplify 0 into 0 1536750507.007 * [misc]backup-simplify: Simplify 1 into 1 1536750507.007 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.007 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750507.007 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.008 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750507.008 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750507.008 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536750507.008 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536750507.009 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536750507.010 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))) 1536750507.010 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536750507.011 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536750507.012 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536750507.017 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 3)))))))) 1536750507.018 * [misc]backup-simplify: Simplify (* (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) into (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 1536750507.018 * [misc]approximate: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in (k n) around 0 1536750507.018 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 1536750507.018 * [misc]taylor: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536750507.018 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750507.018 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536750507.018 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536750507.018 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750507.018 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.018 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.018 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.018 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.018 * [misc]taylor: Taking taylor expansion of k in n 1536750507.018 * [misc]backup-simplify: Simplify k into k 1536750507.018 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.018 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.018 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.018 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536750507.018 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536750507.018 * [misc]taylor: Taking taylor expansion of -1 in n 1536750507.018 * [misc]backup-simplify: Simplify -1 into -1 1536750507.018 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.018 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.018 * [misc]backup-simplify: Simplify PI into PI 1536750507.018 * [misc]taylor: Taking taylor expansion of n in n 1536750507.018 * [misc]backup-simplify: Simplify 0 into 0 1536750507.018 * [misc]backup-simplify: Simplify 1 into 1 1536750507.019 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.019 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536750507.020 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536750507.020 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.020 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750507.020 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536750507.021 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536750507.022 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536750507.022 * [misc]taylor: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750507.022 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in n 1536750507.022 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in n 1536750507.022 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750507.022 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.022 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.022 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.022 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.022 * [misc]taylor: Taking taylor expansion of k in n 1536750507.022 * [misc]backup-simplify: Simplify k into k 1536750507.022 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.022 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.022 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.022 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750507.022 * [misc]taylor: Taking taylor expansion of 2 in n 1536750507.022 * [misc]backup-simplify: Simplify 2 into 2 1536750507.022 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750507.022 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.022 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750507.023 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750507.023 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750507.023 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536750507.023 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536750507.023 * [misc]taylor: Taking taylor expansion of -1 in n 1536750507.023 * [misc]backup-simplify: Simplify -1 into -1 1536750507.023 * [misc]taylor: Taking taylor expansion of k in n 1536750507.023 * [misc]backup-simplify: Simplify k into k 1536750507.023 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536750507.023 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536750507.023 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536750507.023 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536750507.024 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) 1536750507.025 * [misc]backup-simplify: Simplify (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) (sqrt (/ -1 k))) 1536750507.025 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 1536750507.025 * [misc]taylor: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in k 1536750507.025 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750507.025 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k 1536750507.026 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k 1536750507.026 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750507.026 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750507.026 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.026 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.026 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750507.026 * [misc]taylor: Taking taylor expansion of k in k 1536750507.026 * [misc]backup-simplify: Simplify 0 into 0 1536750507.026 * [misc]backup-simplify: Simplify 1 into 1 1536750507.026 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750507.026 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.026 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.026 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in k 1536750507.026 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in k 1536750507.026 * [misc]taylor: Taking taylor expansion of -1 in k 1536750507.026 * [misc]backup-simplify: Simplify -1 into -1 1536750507.026 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750507.026 * [misc]taylor: Taking taylor expansion of PI in k 1536750507.026 * [misc]backup-simplify: Simplify PI into PI 1536750507.026 * [misc]taylor: Taking taylor expansion of n in k 1536750507.026 * [misc]backup-simplify: Simplify n into n 1536750507.026 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750507.026 * [misc]backup-simplify: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 1536750507.026 * [misc]backup-simplify: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 1536750507.027 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750507.027 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750507.027 * [misc]backup-simplify: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n)))) 1536750507.027 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750507.027 * [misc]taylor: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750507.027 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k 1536750507.027 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k 1536750507.027 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750507.027 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750507.027 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.027 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.027 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750507.027 * [misc]taylor: Taking taylor expansion of k in k 1536750507.027 * [misc]backup-simplify: Simplify 0 into 0 1536750507.027 * [misc]backup-simplify: Simplify 1 into 1 1536750507.028 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750507.028 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.028 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.028 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536750507.028 * [misc]taylor: Taking taylor expansion of 2 in k 1536750507.028 * [misc]backup-simplify: Simplify 2 into 2 1536750507.028 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750507.028 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750507.028 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750507.028 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536750507.029 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750507.029 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536750507.029 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536750507.029 * [misc]taylor: Taking taylor expansion of -1 in k 1536750507.029 * [misc]backup-simplify: Simplify -1 into -1 1536750507.029 * [misc]taylor: Taking taylor expansion of k in k 1536750507.029 * [misc]backup-simplify: Simplify 0 into 0 1536750507.029 * [misc]backup-simplify: Simplify 1 into 1 1536750507.029 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750507.029 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750507.030 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536750507.030 * [misc]backup-simplify: Simplify (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750507.030 * [misc]backup-simplify: Simplify (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) +nan.0) into (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) 1536750507.031 * [misc]taylor: Taking taylor expansion of (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 1536750507.031 * [misc]taylor: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (pow 2 (+ (* 1/2 (/ 1 k)) 1/2))) in k 1536750507.031 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750507.031 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k 1536750507.031 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k 1536750507.031 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750507.031 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750507.031 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.031 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.031 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750507.031 * [misc]taylor: Taking taylor expansion of k in k 1536750507.031 * [misc]backup-simplify: Simplify 0 into 0 1536750507.031 * [misc]backup-simplify: Simplify 1 into 1 1536750507.031 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750507.031 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.031 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.031 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in k 1536750507.031 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in k 1536750507.031 * [misc]taylor: Taking taylor expansion of -1 in k 1536750507.031 * [misc]backup-simplify: Simplify -1 into -1 1536750507.031 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750507.031 * [misc]taylor: Taking taylor expansion of PI in k 1536750507.031 * [misc]backup-simplify: Simplify PI into PI 1536750507.031 * [misc]taylor: Taking taylor expansion of n in k 1536750507.031 * [misc]backup-simplify: Simplify n into n 1536750507.031 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750507.032 * [misc]backup-simplify: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 1536750507.032 * [misc]backup-simplify: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 1536750507.032 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750507.032 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750507.032 * [misc]backup-simplify: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n)))) 1536750507.032 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750507.032 * [misc]taylor: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750507.032 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k 1536750507.033 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k 1536750507.033 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750507.033 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750507.033 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.033 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.033 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750507.033 * [misc]taylor: Taking taylor expansion of k in k 1536750507.033 * [misc]backup-simplify: Simplify 0 into 0 1536750507.033 * [misc]backup-simplify: Simplify 1 into 1 1536750507.033 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750507.033 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.033 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.033 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536750507.033 * [misc]taylor: Taking taylor expansion of 2 in k 1536750507.033 * [misc]backup-simplify: Simplify 2 into 2 1536750507.033 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750507.033 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750507.033 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750507.034 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536750507.034 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750507.034 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536750507.034 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536750507.034 * [misc]taylor: Taking taylor expansion of -1 in k 1536750507.034 * [misc]backup-simplify: Simplify -1 into -1 1536750507.034 * [misc]taylor: Taking taylor expansion of k in k 1536750507.034 * [misc]backup-simplify: Simplify 0 into 0 1536750507.034 * [misc]backup-simplify: Simplify 1 into 1 1536750507.034 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750507.034 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750507.035 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536750507.035 * [misc]backup-simplify: Simplify (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750507.036 * [misc]backup-simplify: Simplify (/ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) +nan.0) into (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) 1536750507.036 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1536750507.036 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750507.036 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750507.036 * [misc]taylor: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536750507.036 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750507.036 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536750507.036 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536750507.036 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750507.036 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.036 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.036 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.036 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.036 * [misc]taylor: Taking taylor expansion of k in n 1536750507.036 * [misc]backup-simplify: Simplify k into k 1536750507.036 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.036 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.036 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.036 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536750507.037 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536750507.037 * [misc]taylor: Taking taylor expansion of -1 in n 1536750507.037 * [misc]backup-simplify: Simplify -1 into -1 1536750507.037 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.037 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.037 * [misc]backup-simplify: Simplify PI into PI 1536750507.037 * [misc]taylor: Taking taylor expansion of n in n 1536750507.037 * [misc]backup-simplify: Simplify 0 into 0 1536750507.037 * [misc]backup-simplify: Simplify 1 into 1 1536750507.037 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.037 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536750507.038 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536750507.038 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.038 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750507.039 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536750507.039 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536750507.040 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536750507.040 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536750507.040 * [misc]taylor: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750507.040 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750507.040 * [misc]taylor: Taking taylor expansion of 2 in n 1536750507.040 * [misc]backup-simplify: Simplify 2 into 2 1536750507.040 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750507.040 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750507.040 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.040 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.040 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.040 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.040 * [misc]taylor: Taking taylor expansion of k in n 1536750507.040 * [misc]backup-simplify: Simplify k into k 1536750507.040 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.040 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.040 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.041 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.041 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750507.041 * [misc]backup-simplify: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750507.041 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750507.042 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) 1536750507.043 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536750507.044 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536750507.045 * [misc]backup-simplify: Simplify (+ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1536750507.045 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536750507.046 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750507.047 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536750507.047 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1536750507.047 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1536750507.047 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750507.047 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750507.047 * [misc]taylor: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536750507.047 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750507.047 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536750507.047 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536750507.047 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750507.047 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.047 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.047 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.048 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.048 * [misc]taylor: Taking taylor expansion of k in n 1536750507.048 * [misc]backup-simplify: Simplify k into k 1536750507.048 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.048 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.048 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.048 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536750507.048 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536750507.048 * [misc]taylor: Taking taylor expansion of -1 in n 1536750507.048 * [misc]backup-simplify: Simplify -1 into -1 1536750507.048 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.048 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.048 * [misc]backup-simplify: Simplify PI into PI 1536750507.048 * [misc]taylor: Taking taylor expansion of n in n 1536750507.048 * [misc]backup-simplify: Simplify 0 into 0 1536750507.048 * [misc]backup-simplify: Simplify 1 into 1 1536750507.048 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.049 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536750507.049 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536750507.049 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.049 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750507.050 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536750507.051 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536750507.052 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536750507.052 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536750507.052 * [misc]taylor: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750507.052 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750507.052 * [misc]taylor: Taking taylor expansion of 2 in n 1536750507.052 * [misc]backup-simplify: Simplify 2 into 2 1536750507.052 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750507.052 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750507.052 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.052 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.052 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.052 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.052 * [misc]taylor: Taking taylor expansion of k in n 1536750507.052 * [misc]backup-simplify: Simplify k into k 1536750507.052 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.052 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.052 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.052 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.053 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750507.053 * [misc]backup-simplify: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750507.053 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750507.054 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) 1536750507.056 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536750507.057 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) 1536750507.058 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) 1536750507.058 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750507.058 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750507.059 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.061 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536750507.061 * [misc]backup-simplify: Simplify (+ (* (log 2) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1536750507.063 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750507.064 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750507.065 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 PI)) into 0 1536750507.068 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0 1536750507.068 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750507.068 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750507.068 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.069 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536750507.070 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0 1536750507.072 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750507.073 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1536750507.074 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into 0 1536750507.074 * [misc]backup-simplify: Simplify 0 into 0 1536750507.075 * [misc]backup-simplify: Simplify (+ (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0 1536750507.075 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.076 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750507.078 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536750507.078 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1536750507.078 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1536750507.078 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750507.078 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750507.078 * [misc]taylor: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536750507.078 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750507.078 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536750507.078 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536750507.078 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750507.078 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.078 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.078 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.078 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.078 * [misc]taylor: Taking taylor expansion of k in n 1536750507.078 * [misc]backup-simplify: Simplify k into k 1536750507.078 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.078 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.078 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.078 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536750507.078 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536750507.078 * [misc]taylor: Taking taylor expansion of -1 in n 1536750507.079 * [misc]backup-simplify: Simplify -1 into -1 1536750507.079 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.079 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.079 * [misc]backup-simplify: Simplify PI into PI 1536750507.079 * [misc]taylor: Taking taylor expansion of n in n 1536750507.079 * [misc]backup-simplify: Simplify 0 into 0 1536750507.079 * [misc]backup-simplify: Simplify 1 into 1 1536750507.079 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.079 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536750507.080 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536750507.080 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.080 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750507.081 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536750507.081 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536750507.082 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536750507.082 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536750507.082 * [misc]taylor: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750507.082 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750507.082 * [misc]taylor: Taking taylor expansion of 2 in n 1536750507.082 * [misc]backup-simplify: Simplify 2 into 2 1536750507.083 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750507.083 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750507.083 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.083 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.083 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.083 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.083 * [misc]taylor: Taking taylor expansion of k in n 1536750507.083 * [misc]backup-simplify: Simplify k into k 1536750507.083 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.083 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.083 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.083 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.083 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750507.083 * [misc]backup-simplify: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750507.083 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750507.084 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) 1536750507.085 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536750507.085 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) 1536750507.086 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))))) 1536750507.089 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))))))))) 1536750507.089 * * * * [misc]progress: [ 2 / 4 ] generating series at (2 2 1) 1536750507.089 * [misc]backup-simplify: Simplify (pow (* n PI) (- 1/2 (/ k 2))) into (pow (* n PI) (- 1/2 (* 1/2 k))) 1536750507.089 * [misc]approximate: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in (n k) around 0 1536750507.089 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k 1536750507.089 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k 1536750507.089 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k 1536750507.089 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750507.089 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.089 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.089 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750507.089 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.089 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.089 * [misc]taylor: Taking taylor expansion of k in k 1536750507.089 * [misc]backup-simplify: Simplify 0 into 0 1536750507.089 * [misc]backup-simplify: Simplify 1 into 1 1536750507.089 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in k 1536750507.089 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536750507.089 * [misc]taylor: Taking taylor expansion of n in k 1536750507.089 * [misc]backup-simplify: Simplify n into n 1536750507.089 * [misc]taylor: Taking taylor expansion of PI in k 1536750507.089 * [misc]backup-simplify: Simplify PI into PI 1536750507.090 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536750507.090 * [misc]backup-simplify: Simplify (log (* n PI)) into (log (* n PI)) 1536750507.090 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750507.090 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.090 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750507.090 * [misc]backup-simplify: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI))) 1536750507.090 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2) 1536750507.090 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n 1536750507.090 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n 1536750507.090 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n 1536750507.090 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750507.090 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.090 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.090 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750507.090 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.090 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.090 * [misc]taylor: Taking taylor expansion of k in n 1536750507.090 * [misc]backup-simplify: Simplify k into k 1536750507.090 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536750507.090 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750507.090 * [misc]taylor: Taking taylor expansion of n in n 1536750507.090 * [misc]backup-simplify: Simplify 0 into 0 1536750507.090 * [misc]backup-simplify: Simplify 1 into 1 1536750507.090 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.090 * [misc]backup-simplify: Simplify PI into PI 1536750507.091 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750507.091 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750507.091 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750507.091 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750507.091 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750507.091 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750507.092 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750507.092 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) 1536750507.092 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 1536750507.092 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n 1536750507.092 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n 1536750507.092 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n 1536750507.092 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750507.092 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.092 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.092 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750507.092 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.092 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.092 * [misc]taylor: Taking taylor expansion of k in n 1536750507.092 * [misc]backup-simplify: Simplify k into k 1536750507.092 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536750507.092 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750507.092 * [misc]taylor: Taking taylor expansion of n in n 1536750507.092 * [misc]backup-simplify: Simplify 0 into 0 1536750507.092 * [misc]backup-simplify: Simplify 1 into 1 1536750507.092 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.093 * [misc]backup-simplify: Simplify PI into PI 1536750507.093 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750507.093 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750507.093 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750507.093 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750507.093 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750507.093 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750507.094 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750507.094 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) 1536750507.094 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 1536750507.094 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) in k 1536750507.094 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) in k 1536750507.094 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750507.094 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.094 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.094 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750507.094 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.094 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.094 * [misc]taylor: Taking taylor expansion of k in k 1536750507.095 * [misc]backup-simplify: Simplify 0 into 0 1536750507.095 * [misc]backup-simplify: Simplify 1 into 1 1536750507.095 * [misc]taylor: Taking taylor expansion of (+ (log PI) (log n)) in k 1536750507.095 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750507.095 * [misc]taylor: Taking taylor expansion of PI in k 1536750507.095 * [misc]backup-simplify: Simplify PI into PI 1536750507.095 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750507.095 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750507.095 * [misc]taylor: Taking taylor expansion of n in k 1536750507.095 * [misc]backup-simplify: Simplify n into n 1536750507.095 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750507.095 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750507.095 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.095 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750507.095 * [misc]backup-simplify: Simplify (+ (log PI) (log n)) into (+ (log PI) (log n)) 1536750507.096 * [misc]backup-simplify: Simplify (* 1/2 (+ (log PI) (log n))) into (* 1/2 (+ (log PI) (log n))) 1536750507.096 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log PI) (log n)))) into (exp (* 1/2 (+ (log PI) (log n)))) 1536750507.096 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log PI) (log n)))) into (exp (* 1/2 (+ (log PI) (log n)))) 1536750507.097 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536750507.098 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750507.099 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536750507.099 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.099 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.099 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750507.099 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log PI) (log n)))) into 0 1536750507.100 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750507.100 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.100 * [misc]backup-simplify: Simplify 0 into 0 1536750507.100 * [misc]backup-simplify: Simplify 0 into 0 1536750507.102 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750507.103 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536750507.103 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.103 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536750507.103 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750507.103 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750507.103 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log PI) (log n)))) into (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1536750507.104 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) 1536750507.105 * [misc]backup-simplify: Simplify (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) 1536750507.106 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750507.109 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536750507.109 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536750507.110 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.110 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.110 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750507.110 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log PI) (log n))))) into 0 1536750507.112 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750507.112 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.112 * [misc]backup-simplify: Simplify 0 into 0 1536750507.112 * [misc]backup-simplify: Simplify 0 into 0 1536750507.112 * [misc]backup-simplify: Simplify 0 into 0 1536750507.115 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536750507.116 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536750507.116 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.116 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536750507.116 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.116 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.117 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log PI) (log n))))) into 0 1536750507.119 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) 1536750507.121 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) into (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) 1536750507.125 * [misc]backup-simplify: Simplify (+ (* (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log PI) (log n)))))) into (- (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (exp (* 1/2 (+ (log PI) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))))) 1536750507.125 * [misc]backup-simplify: Simplify (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) 1536750507.125 * [misc]approximate: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 1536750507.125 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750507.125 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k 1536750507.125 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k 1536750507.125 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750507.125 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.125 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.125 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750507.125 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.125 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.125 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750507.125 * [misc]taylor: Taking taylor expansion of k in k 1536750507.125 * [misc]backup-simplify: Simplify 0 into 0 1536750507.125 * [misc]backup-simplify: Simplify 1 into 1 1536750507.125 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750507.125 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in k 1536750507.125 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750507.125 * [misc]taylor: Taking taylor expansion of PI in k 1536750507.125 * [misc]backup-simplify: Simplify PI into PI 1536750507.125 * [misc]taylor: Taking taylor expansion of n in k 1536750507.125 * [misc]backup-simplify: Simplify n into n 1536750507.125 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750507.125 * [misc]backup-simplify: Simplify (log (/ PI n)) into (log (/ PI n)) 1536750507.126 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750507.126 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750507.126 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750507.126 * [misc]backup-simplify: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n))) 1536750507.126 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) 1536750507.126 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750507.126 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536750507.126 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536750507.126 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750507.126 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.126 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.126 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.126 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.126 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.126 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.126 * [misc]taylor: Taking taylor expansion of k in n 1536750507.126 * [misc]backup-simplify: Simplify k into k 1536750507.126 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.126 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536750507.126 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.126 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.126 * [misc]backup-simplify: Simplify PI into PI 1536750507.126 * [misc]taylor: Taking taylor expansion of n in n 1536750507.126 * [misc]backup-simplify: Simplify 0 into 0 1536750507.126 * [misc]backup-simplify: Simplify 1 into 1 1536750507.127 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.127 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750507.127 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.127 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750507.127 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750507.127 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536750507.128 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536750507.128 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536750507.128 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750507.128 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536750507.128 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536750507.128 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750507.128 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.128 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.128 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.128 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.128 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.128 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.128 * [misc]taylor: Taking taylor expansion of k in n 1536750507.128 * [misc]backup-simplify: Simplify k into k 1536750507.128 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.128 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536750507.128 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.128 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.128 * [misc]backup-simplify: Simplify PI into PI 1536750507.128 * [misc]taylor: Taking taylor expansion of n in n 1536750507.128 * [misc]backup-simplify: Simplify 0 into 0 1536750507.128 * [misc]backup-simplify: Simplify 1 into 1 1536750507.128 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.129 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750507.129 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.129 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750507.129 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750507.129 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536750507.129 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536750507.130 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536750507.130 * [misc]taylor: Taking taylor expansion of (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536750507.130 * [misc]taylor: Taking taylor expansion of (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750507.130 * [misc]taylor: Taking taylor expansion of (- (log PI) (log n)) in k 1536750507.130 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750507.130 * [misc]taylor: Taking taylor expansion of PI in k 1536750507.130 * [misc]backup-simplify: Simplify PI into PI 1536750507.130 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750507.130 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750507.130 * [misc]taylor: Taking taylor expansion of n in k 1536750507.130 * [misc]backup-simplify: Simplify n into n 1536750507.130 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750507.130 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750507.130 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.130 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.130 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750507.130 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.130 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.130 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750507.130 * [misc]taylor: Taking taylor expansion of k in k 1536750507.130 * [misc]backup-simplify: Simplify 0 into 0 1536750507.130 * [misc]backup-simplify: Simplify 1 into 1 1536750507.130 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750507.131 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536750507.131 * [misc]backup-simplify: Simplify (+ (log PI) (- (log n))) into (- (log PI) (log n)) 1536750507.131 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750507.131 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750507.131 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750507.131 * [misc]backup-simplify: Simplify (* (- (log PI) (log n)) -1/2) into (* -1/2 (- (log PI) (log n))) 1536750507.132 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536750507.132 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536750507.133 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750507.134 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750507.134 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750507.134 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750507.135 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.135 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.135 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536750507.135 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0 1536750507.136 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750507.136 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.136 * [misc]backup-simplify: Simplify 0 into 0 1536750507.136 * [misc]backup-simplify: Simplify 0 into 0 1536750507.136 * [misc]backup-simplify: Simplify 0 into 0 1536750507.139 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.142 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536750507.142 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750507.142 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750507.143 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.143 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.143 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536750507.144 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0 1536750507.146 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750507.146 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.146 * [misc]backup-simplify: Simplify 0 into 0 1536750507.146 * [misc]backup-simplify: Simplify 0 into 0 1536750507.146 * [misc]backup-simplify: Simplify 0 into 0 1536750507.146 * [misc]backup-simplify: Simplify 0 into 0 1536750507.148 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.152 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536750507.152 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750507.152 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536750507.153 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.153 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.153 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536750507.154 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0 1536750507.156 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750507.156 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.156 * [misc]backup-simplify: Simplify 0 into 0 1536750507.156 * [misc]backup-simplify: Simplify 0 into 0 1536750507.156 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) 1536750507.156 * [misc]backup-simplify: Simplify (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750507.156 * [misc]approximate: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 1536750507.156 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750507.156 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k 1536750507.156 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k 1536750507.156 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750507.156 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750507.156 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.156 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.156 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750507.156 * [misc]taylor: Taking taylor expansion of k in k 1536750507.156 * [misc]backup-simplify: Simplify 0 into 0 1536750507.156 * [misc]backup-simplify: Simplify 1 into 1 1536750507.156 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750507.157 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.157 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.157 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in k 1536750507.157 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in k 1536750507.157 * [misc]taylor: Taking taylor expansion of -1 in k 1536750507.157 * [misc]backup-simplify: Simplify -1 into -1 1536750507.157 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750507.157 * [misc]taylor: Taking taylor expansion of PI in k 1536750507.157 * [misc]backup-simplify: Simplify PI into PI 1536750507.157 * [misc]taylor: Taking taylor expansion of n in k 1536750507.157 * [misc]backup-simplify: Simplify n into n 1536750507.157 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750507.157 * [misc]backup-simplify: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 1536750507.157 * [misc]backup-simplify: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 1536750507.157 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750507.157 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750507.157 * [misc]backup-simplify: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n)))) 1536750507.157 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750507.157 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750507.157 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536750507.157 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536750507.157 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750507.158 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.158 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.158 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.158 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.158 * [misc]taylor: Taking taylor expansion of k in n 1536750507.158 * [misc]backup-simplify: Simplify k into k 1536750507.158 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.158 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.158 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.158 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536750507.158 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536750507.158 * [misc]taylor: Taking taylor expansion of -1 in n 1536750507.158 * [misc]backup-simplify: Simplify -1 into -1 1536750507.158 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.158 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.158 * [misc]backup-simplify: Simplify PI into PI 1536750507.158 * [misc]taylor: Taking taylor expansion of n in n 1536750507.158 * [misc]backup-simplify: Simplify 0 into 0 1536750507.158 * [misc]backup-simplify: Simplify 1 into 1 1536750507.158 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.159 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536750507.159 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536750507.159 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.159 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750507.159 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536750507.160 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536750507.160 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536750507.160 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750507.160 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536750507.160 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536750507.160 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750507.160 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.160 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.160 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.160 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.160 * [misc]taylor: Taking taylor expansion of k in n 1536750507.160 * [misc]backup-simplify: Simplify k into k 1536750507.161 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.161 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.161 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.161 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536750507.161 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536750507.161 * [misc]taylor: Taking taylor expansion of -1 in n 1536750507.161 * [misc]backup-simplify: Simplify -1 into -1 1536750507.161 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.161 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.161 * [misc]backup-simplify: Simplify PI into PI 1536750507.161 * [misc]taylor: Taking taylor expansion of n in n 1536750507.161 * [misc]backup-simplify: Simplify 0 into 0 1536750507.161 * [misc]backup-simplify: Simplify 1 into 1 1536750507.161 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.161 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536750507.161 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536750507.161 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.162 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750507.162 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536750507.162 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536750507.163 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536750507.163 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) in k 1536750507.163 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) in k 1536750507.163 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750507.163 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750507.163 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.163 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.163 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750507.163 * [misc]taylor: Taking taylor expansion of k in k 1536750507.163 * [misc]backup-simplify: Simplify 0 into 0 1536750507.163 * [misc]backup-simplify: Simplify 1 into 1 1536750507.163 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750507.163 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.163 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.163 * [misc]taylor: Taking taylor expansion of (- (log (* -1 PI)) (log n)) in k 1536750507.163 * [misc]taylor: Taking taylor expansion of (log (* -1 PI)) in k 1536750507.163 * [misc]taylor: Taking taylor expansion of (* -1 PI) in k 1536750507.163 * [misc]taylor: Taking taylor expansion of -1 in k 1536750507.163 * [misc]backup-simplify: Simplify -1 into -1 1536750507.163 * [misc]taylor: Taking taylor expansion of PI in k 1536750507.163 * [misc]backup-simplify: Simplify PI into PI 1536750507.164 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536750507.164 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536750507.164 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750507.164 * [misc]taylor: Taking taylor expansion of n in k 1536750507.164 * [misc]backup-simplify: Simplify n into n 1536750507.164 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750507.164 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750507.164 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750507.164 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536750507.165 * [misc]backup-simplify: Simplify (+ (log (* -1 PI)) (- (log n))) into (- (log (* -1 PI)) (log n)) 1536750507.165 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -1 PI)) (log n))) into (* 1/2 (- (log (* -1 PI)) (log n))) 1536750507.165 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536750507.166 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536750507.167 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750507.167 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 PI)) into 0 1536750507.169 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0 1536750507.169 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750507.169 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750507.169 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.170 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536750507.170 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0 1536750507.171 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750507.171 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.171 * [misc]backup-simplify: Simplify 0 into 0 1536750507.171 * [misc]backup-simplify: Simplify 0 into 0 1536750507.171 * [misc]backup-simplify: Simplify 0 into 0 1536750507.172 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.173 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 1536750507.176 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 PI) 1)))) 2) into 0 1536750507.176 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750507.177 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750507.177 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.177 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536750507.178 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0 1536750507.179 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750507.179 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.179 * [misc]backup-simplify: Simplify 0 into 0 1536750507.179 * [misc]backup-simplify: Simplify 0 into 0 1536750507.179 * [misc]backup-simplify: Simplify 0 into 0 1536750507.179 * [misc]backup-simplify: Simplify 0 into 0 1536750507.181 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.183 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750507.192 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -1 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -1 PI) 1)))) 6) into 0 1536750507.192 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750507.193 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536750507.193 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.193 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536750507.194 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n)))))) into 0 1536750507.198 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750507.198 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.198 * [misc]backup-simplify: Simplify 0 into 0 1536750507.198 * [misc]backup-simplify: Simplify 0 into 0 1536750507.199 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))) into (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) 1536750507.199 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2 1 1) 1536750507.200 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536750507.200 * [misc]approximate: Taking taylor expansion of (* n PI) in (n) around 0 1536750507.200 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750507.200 * [misc]taylor: Taking taylor expansion of n in n 1536750507.200 * [misc]backup-simplify: Simplify 0 into 0 1536750507.200 * [misc]backup-simplify: Simplify 1 into 1 1536750507.200 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.200 * [misc]backup-simplify: Simplify PI into PI 1536750507.200 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750507.200 * [misc]taylor: Taking taylor expansion of n in n 1536750507.200 * [misc]backup-simplify: Simplify 0 into 0 1536750507.200 * [misc]backup-simplify: Simplify 1 into 1 1536750507.200 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.200 * [misc]backup-simplify: Simplify PI into PI 1536750507.201 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750507.201 * [misc]backup-simplify: Simplify 0 into 0 1536750507.201 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750507.201 * [misc]backup-simplify: Simplify PI into PI 1536750507.203 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536750507.203 * [misc]backup-simplify: Simplify 0 into 0 1536750507.204 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750507.204 * [misc]backup-simplify: Simplify 0 into 0 1536750507.206 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536750507.206 * [misc]backup-simplify: Simplify 0 into 0 1536750507.209 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536750507.209 * [misc]backup-simplify: Simplify 0 into 0 1536750507.213 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536750507.213 * [misc]backup-simplify: Simplify 0 into 0 1536750507.217 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1536750507.217 * [misc]backup-simplify: Simplify 0 into 0 1536750507.217 * [misc]backup-simplify: Simplify (* PI n) into (* n PI) 1536750507.217 * [misc]backup-simplify: Simplify (* (/ 1 n) PI) into (/ PI n) 1536750507.217 * [misc]approximate: Taking taylor expansion of (/ PI n) in (n) around 0 1536750507.218 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.218 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.218 * [misc]backup-simplify: Simplify PI into PI 1536750507.218 * [misc]taylor: Taking taylor expansion of n in n 1536750507.218 * [misc]backup-simplify: Simplify 0 into 0 1536750507.218 * [misc]backup-simplify: Simplify 1 into 1 1536750507.218 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.218 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.218 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.218 * [misc]backup-simplify: Simplify PI into PI 1536750507.218 * [misc]taylor: Taking taylor expansion of n in n 1536750507.218 * [misc]backup-simplify: Simplify 0 into 0 1536750507.218 * [misc]backup-simplify: Simplify 1 into 1 1536750507.219 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.219 * [misc]backup-simplify: Simplify PI into PI 1536750507.220 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750507.220 * [misc]backup-simplify: Simplify 0 into 0 1536750507.221 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.221 * [misc]backup-simplify: Simplify 0 into 0 1536750507.223 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.223 * [misc]backup-simplify: Simplify 0 into 0 1536750507.225 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.225 * [misc]backup-simplify: Simplify 0 into 0 1536750507.227 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.227 * [misc]backup-simplify: Simplify 0 into 0 1536750507.230 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.230 * [misc]backup-simplify: Simplify 0 into 0 1536750507.230 * [misc]backup-simplify: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 1536750507.230 * [misc]backup-simplify: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 1536750507.230 * [misc]approximate: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 1536750507.230 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536750507.230 * [misc]taylor: Taking taylor expansion of -1 in n 1536750507.230 * [misc]backup-simplify: Simplify -1 into -1 1536750507.230 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.230 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.230 * [misc]backup-simplify: Simplify PI into PI 1536750507.230 * [misc]taylor: Taking taylor expansion of n in n 1536750507.230 * [misc]backup-simplify: Simplify 0 into 0 1536750507.230 * [misc]backup-simplify: Simplify 1 into 1 1536750507.231 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.231 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536750507.231 * [misc]taylor: Taking taylor expansion of -1 in n 1536750507.231 * [misc]backup-simplify: Simplify -1 into -1 1536750507.231 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.231 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.231 * [misc]backup-simplify: Simplify PI into PI 1536750507.231 * [misc]taylor: Taking taylor expansion of n in n 1536750507.231 * [misc]backup-simplify: Simplify 0 into 0 1536750507.231 * [misc]backup-simplify: Simplify 1 into 1 1536750507.231 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.231 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536750507.232 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536750507.233 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750507.234 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 PI)) into 0 1536750507.234 * [misc]backup-simplify: Simplify 0 into 0 1536750507.235 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.236 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 1536750507.236 * [misc]backup-simplify: Simplify 0 into 0 1536750507.238 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.239 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750507.239 * [misc]backup-simplify: Simplify 0 into 0 1536750507.241 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.243 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536750507.243 * [misc]backup-simplify: Simplify 0 into 0 1536750507.246 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.248 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1536750507.248 * [misc]backup-simplify: Simplify 0 into 0 1536750507.249 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.251 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1536750507.251 * [misc]backup-simplify: Simplify 0 into 0 1536750507.252 * [misc]backup-simplify: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 1536750507.252 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2) 1536750507.252 * [misc]backup-simplify: Simplify (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) into (* (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 1536750507.252 * [misc]approximate: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (n k) around 0 1536750507.252 * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 1536750507.252 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in k 1536750507.252 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in k 1536750507.252 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in k 1536750507.252 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750507.252 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.252 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.252 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750507.252 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.252 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.252 * [misc]taylor: Taking taylor expansion of k in k 1536750507.252 * [misc]backup-simplify: Simplify 0 into 0 1536750507.252 * [misc]backup-simplify: Simplify 1 into 1 1536750507.252 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in k 1536750507.252 * [misc]taylor: Taking taylor expansion of (* n PI) in k 1536750507.252 * [misc]taylor: Taking taylor expansion of n in k 1536750507.252 * [misc]backup-simplify: Simplify n into n 1536750507.252 * [misc]taylor: Taking taylor expansion of PI in k 1536750507.253 * [misc]backup-simplify: Simplify PI into PI 1536750507.253 * [misc]backup-simplify: Simplify (* n PI) into (* n PI) 1536750507.253 * [misc]backup-simplify: Simplify (log (* n PI)) into (log (* n PI)) 1536750507.253 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750507.253 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.253 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750507.253 * [misc]backup-simplify: Simplify (* 1/2 (log (* n PI))) into (* 1/2 (log (* n PI))) 1536750507.253 * [misc]backup-simplify: Simplify (exp (* 1/2 (log (* n PI)))) into (pow (* n PI) 1/2) 1536750507.253 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536750507.253 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750507.253 * [misc]taylor: Taking taylor expansion of k in k 1536750507.253 * [misc]backup-simplify: Simplify 0 into 0 1536750507.253 * [misc]backup-simplify: Simplify 1 into 1 1536750507.253 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750507.253 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750507.254 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750507.254 * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 1536750507.254 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n 1536750507.254 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n 1536750507.254 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n 1536750507.254 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750507.254 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.254 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.254 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750507.254 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.254 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.254 * [misc]taylor: Taking taylor expansion of k in n 1536750507.254 * [misc]backup-simplify: Simplify k into k 1536750507.254 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536750507.254 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750507.254 * [misc]taylor: Taking taylor expansion of n in n 1536750507.254 * [misc]backup-simplify: Simplify 0 into 0 1536750507.254 * [misc]backup-simplify: Simplify 1 into 1 1536750507.254 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.254 * [misc]backup-simplify: Simplify PI into PI 1536750507.254 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750507.255 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750507.255 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750507.255 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750507.255 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750507.255 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750507.255 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750507.256 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) 1536750507.256 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 1536750507.256 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536750507.256 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.256 * [misc]taylor: Taking taylor expansion of k in n 1536750507.256 * [misc]backup-simplify: Simplify k into k 1536750507.256 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.256 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536750507.256 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750507.256 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536750507.256 * [misc]taylor: Taking taylor expansion of (* (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 1536750507.256 * [misc]taylor: Taking taylor expansion of (pow (* n PI) (- 1/2 (* 1/2 k))) in n 1536750507.256 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* n PI)))) in n 1536750507.256 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* n PI))) in n 1536750507.256 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750507.256 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.256 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.256 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750507.256 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.256 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.256 * [misc]taylor: Taking taylor expansion of k in n 1536750507.257 * [misc]backup-simplify: Simplify k into k 1536750507.257 * [misc]taylor: Taking taylor expansion of (log (* n PI)) in n 1536750507.257 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750507.257 * [misc]taylor: Taking taylor expansion of n in n 1536750507.257 * [misc]backup-simplify: Simplify 0 into 0 1536750507.257 * [misc]backup-simplify: Simplify 1 into 1 1536750507.257 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.257 * [misc]backup-simplify: Simplify PI into PI 1536750507.257 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750507.257 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750507.257 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750507.258 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750507.258 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750507.258 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750507.258 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750507.258 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) into (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) 1536750507.259 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 1536750507.259 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536750507.259 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.259 * [misc]taylor: Taking taylor expansion of k in n 1536750507.259 * [misc]backup-simplify: Simplify k into k 1536750507.259 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.259 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536750507.259 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750507.259 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536750507.259 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k))) 1536750507.259 * [misc]taylor: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (sqrt (/ 1 k))) in k 1536750507.259 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) in k 1536750507.259 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n))) in k 1536750507.259 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750507.259 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.259 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.259 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750507.259 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.259 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.259 * [misc]taylor: Taking taylor expansion of k in k 1536750507.259 * [misc]backup-simplify: Simplify 0 into 0 1536750507.259 * [misc]backup-simplify: Simplify 1 into 1 1536750507.259 * [misc]taylor: Taking taylor expansion of (+ (log PI) (log n)) in k 1536750507.259 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750507.260 * [misc]taylor: Taking taylor expansion of PI in k 1536750507.260 * [misc]backup-simplify: Simplify PI into PI 1536750507.260 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750507.260 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750507.260 * [misc]taylor: Taking taylor expansion of n in k 1536750507.260 * [misc]backup-simplify: Simplify n into n 1536750507.260 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750507.260 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750507.260 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.260 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750507.261 * [misc]backup-simplify: Simplify (+ (log PI) (log n)) into (+ (log PI) (log n)) 1536750507.262 * [misc]backup-simplify: Simplify (* 1/2 (+ (log PI) (log n))) into (* 1/2 (+ (log PI) (log n))) 1536750507.262 * [misc]backup-simplify: Simplify (exp (* 1/2 (+ (log PI) (log n)))) into (exp (* 1/2 (+ (log PI) (log n)))) 1536750507.262 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536750507.262 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750507.262 * [misc]taylor: Taking taylor expansion of k in k 1536750507.262 * [misc]backup-simplify: Simplify 0 into 0 1536750507.262 * [misc]backup-simplify: Simplify 1 into 1 1536750507.262 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750507.262 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750507.262 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750507.263 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) 0) into 0 1536750507.263 * [misc]backup-simplify: Simplify 0 into 0 1536750507.264 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536750507.265 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750507.265 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536750507.265 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.266 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.266 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750507.266 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log PI) (log n)))) into 0 1536750507.267 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750507.268 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 0) (* 0 (sqrt (/ 1 k)))) into 0 1536750507.268 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.268 * [misc]backup-simplify: Simplify 0 into 0 1536750507.270 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750507.270 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536750507.270 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.270 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536750507.271 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750507.271 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750507.271 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (+ (log PI) (log n)))) into (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1536750507.272 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) 1536750507.273 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log PI) (log n)))) +nan.0) (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n)))))) 1536750507.273 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n)))))) 1536750507.273 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750507.274 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1536750507.275 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1536750507.279 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536750507.279 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536750507.279 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.280 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.280 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750507.281 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log PI) (log n))))) into 0 1536750507.282 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750507.283 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 1536750507.283 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.283 * [misc]backup-simplify: Simplify 0 into 0 1536750507.283 * [misc]backup-simplify: Simplify 0 into 0 1536750507.284 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536750507.284 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750507.289 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536750507.291 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536750507.291 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.291 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536750507.292 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.292 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.293 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log PI) (log n))))) into 0 1536750507.296 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) 1536750507.301 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log PI) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) +nan.0) (* (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n)))))))) 1536750507.303 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n)))))))) 1536750507.304 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750507.304 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1536750507.306 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1536750507.314 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536750507.315 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1536750507.315 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.315 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.316 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 1536750507.317 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log PI) (log n)))))) into 0 1536750507.321 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750507.321 * [misc]backup-simplify: Simplify (+ (* (exp (* (- 1/2 (* 1/2 k)) (+ (log PI) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 1536750507.322 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.322 * [misc]backup-simplify: Simplify 0 into 0 1536750507.322 * [misc]backup-simplify: Simplify 0 into 0 1536750507.322 * [misc]backup-simplify: Simplify 0 into 0 1536750507.322 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.323 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750507.331 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536750507.333 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 1536750507.333 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.333 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536750507.334 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.334 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.334 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log PI) (log n)))))) into 0 1536750507.338 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log PI)) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/48 (pow (log PI) 3)) (+ (* 1/16 (* (pow (log PI) 2) (log n))) (* 1/16 (* (log PI) (pow (log n) 2)))))) (exp (* 1/2 (+ (log PI) (log n)))))) 1536750507.347 * [misc]backup-simplify: Simplify (+ (* (exp (* 1/2 (+ (log PI) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/2 (log PI)) (* 1/2 (log n))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log PI) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/8 (pow (log PI) 2)) (* 1/4 (* (log PI) (log n)))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/48 (pow (log PI) 3)) (+ (* 1/16 (* (pow (log PI) 2) (log n))) (* 1/16 (* (log PI) (pow (log n) 2)))))) (exp (* 1/2 (+ (log PI) (log n)))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2)))))))))))))) 1536750507.355 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2)))))))))))))) 1536750507.372 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (log n)))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow (log PI) 2)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log PI))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log PI) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (pow k 2))))))))))))))))))))))) 1536750507.373 * [misc]backup-simplify: Simplify (/ (pow (* (/ 1 n) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 1536750507.373 * [misc]approximate: Taking taylor expansion of (* (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (n k) around 0 1536750507.373 * [misc]taylor: Taking taylor expansion of (* (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 1536750507.373 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750507.373 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in k 1536750507.373 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in k 1536750507.373 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750507.373 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.373 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.373 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750507.373 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.373 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.373 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750507.373 * [misc]taylor: Taking taylor expansion of k in k 1536750507.373 * [misc]backup-simplify: Simplify 0 into 0 1536750507.373 * [misc]backup-simplify: Simplify 1 into 1 1536750507.373 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750507.373 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in k 1536750507.373 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750507.373 * [misc]taylor: Taking taylor expansion of PI in k 1536750507.373 * [misc]backup-simplify: Simplify PI into PI 1536750507.374 * [misc]taylor: Taking taylor expansion of n in k 1536750507.374 * [misc]backup-simplify: Simplify n into n 1536750507.374 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750507.374 * [misc]backup-simplify: Simplify (log (/ PI n)) into (log (/ PI n)) 1536750507.374 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750507.374 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750507.374 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750507.374 * [misc]backup-simplify: Simplify (* -1/2 (log (/ PI n))) into (* -1/2 (log (/ PI n))) 1536750507.375 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) into (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) 1536750507.375 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536750507.375 * [misc]taylor: Taking taylor expansion of k in k 1536750507.375 * [misc]backup-simplify: Simplify 0 into 0 1536750507.375 * [misc]backup-simplify: Simplify 1 into 1 1536750507.375 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750507.376 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750507.376 * [misc]taylor: Taking taylor expansion of (* (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 1536750507.376 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750507.376 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536750507.376 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536750507.376 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750507.376 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.376 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.376 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.376 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.376 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.376 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.376 * [misc]taylor: Taking taylor expansion of k in n 1536750507.376 * [misc]backup-simplify: Simplify k into k 1536750507.376 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.376 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536750507.376 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.376 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.376 * [misc]backup-simplify: Simplify PI into PI 1536750507.376 * [misc]taylor: Taking taylor expansion of n in n 1536750507.376 * [misc]backup-simplify: Simplify 0 into 0 1536750507.376 * [misc]backup-simplify: Simplify 1 into 1 1536750507.377 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.377 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750507.377 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.377 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750507.378 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750507.378 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536750507.379 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536750507.379 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536750507.379 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536750507.379 * [misc]taylor: Taking taylor expansion of k in n 1536750507.379 * [misc]backup-simplify: Simplify k into k 1536750507.379 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536750507.379 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536750507.379 * [misc]taylor: Taking taylor expansion of (* (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 1536750507.379 * [misc]taylor: Taking taylor expansion of (pow (/ PI n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750507.379 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n)))) in n 1536750507.379 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ PI n))) in n 1536750507.380 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750507.380 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.380 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.380 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.380 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.380 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.380 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.380 * [misc]taylor: Taking taylor expansion of k in n 1536750507.380 * [misc]backup-simplify: Simplify k into k 1536750507.380 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.380 * [misc]taylor: Taking taylor expansion of (log (/ PI n)) in n 1536750507.380 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.380 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.380 * [misc]backup-simplify: Simplify PI into PI 1536750507.380 * [misc]taylor: Taking taylor expansion of n in n 1536750507.380 * [misc]backup-simplify: Simplify 0 into 0 1536750507.380 * [misc]backup-simplify: Simplify 1 into 1 1536750507.380 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.381 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750507.381 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.381 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750507.381 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750507.382 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536750507.382 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log PI) (log n))) into (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) 1536750507.382 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536750507.383 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536750507.383 * [misc]taylor: Taking taylor expansion of k in n 1536750507.383 * [misc]backup-simplify: Simplify k into k 1536750507.383 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536750507.383 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536750507.383 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) into (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 1536750507.383 * [misc]taylor: Taking taylor expansion of (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1536750507.383 * [misc]taylor: Taking taylor expansion of (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536750507.383 * [misc]taylor: Taking taylor expansion of (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750507.384 * [misc]taylor: Taking taylor expansion of (- (log PI) (log n)) in k 1536750507.384 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750507.384 * [misc]taylor: Taking taylor expansion of PI in k 1536750507.384 * [misc]backup-simplify: Simplify PI into PI 1536750507.384 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750507.384 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750507.384 * [misc]taylor: Taking taylor expansion of n in k 1536750507.384 * [misc]backup-simplify: Simplify n into n 1536750507.384 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750507.384 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750507.384 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.384 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.384 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750507.384 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.384 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.384 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750507.384 * [misc]taylor: Taking taylor expansion of k in k 1536750507.384 * [misc]backup-simplify: Simplify 0 into 0 1536750507.384 * [misc]backup-simplify: Simplify 1 into 1 1536750507.385 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750507.385 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536750507.385 * [misc]backup-simplify: Simplify (+ (log PI) (- (log n))) into (- (log PI) (log n)) 1536750507.385 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750507.385 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750507.385 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750507.386 * [misc]backup-simplify: Simplify (* (- (log PI) (log n)) -1/2) into (* -1/2 (- (log PI) (log n))) 1536750507.386 * [misc]backup-simplify: Simplify (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 1536750507.386 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536750507.386 * [misc]taylor: Taking taylor expansion of k in k 1536750507.386 * [misc]backup-simplify: Simplify 0 into 0 1536750507.386 * [misc]backup-simplify: Simplify 1 into 1 1536750507.387 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750507.387 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750507.388 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1536750507.388 * [misc]backup-simplify: Simplify 0 into 0 1536750507.389 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750507.394 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750507.395 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750507.395 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750507.395 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.395 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.396 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536750507.396 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0 1536750507.398 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750507.398 * [misc]backup-simplify: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (sqrt k))) into 0 1536750507.398 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.398 * [misc]backup-simplify: Simplify 0 into 0 1536750507.398 * [misc]backup-simplify: Simplify 0 into 0 1536750507.399 * [misc]backup-simplify: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536750507.400 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536750507.400 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1536750507.402 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.407 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536750507.407 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750507.408 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750507.408 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.408 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.408 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536750507.409 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0 1536750507.411 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750507.412 * [misc]backup-simplify: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 1536750507.412 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.412 * [misc]backup-simplify: Simplify 0 into 0 1536750507.412 * [misc]backup-simplify: Simplify 0 into 0 1536750507.412 * [misc]backup-simplify: Simplify 0 into 0 1536750507.413 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750507.414 * [misc]backup-simplify: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536750507.415 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536750507.415 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1536750507.416 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.421 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536750507.421 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750507.421 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536750507.422 * [misc]backup-simplify: Simplify (- 0) into 0 1536750507.422 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.422 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 1536750507.422 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0 1536750507.425 * [misc]backup-simplify: Simplify (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750507.425 * [misc]backup-simplify: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 1536750507.425 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.425 * [misc]backup-simplify: Simplify 0 into 0 1536750507.425 * [misc]backup-simplify: Simplify 0 into 0 1536750507.425 * [misc]backup-simplify: Simplify 0 into 0 1536750507.425 * [misc]backup-simplify: Simplify 0 into 0 1536750507.426 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750507.427 * [misc]backup-simplify: Simplify (+ (* (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536750507.427 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (exp (* (- (log PI) (log n)) (- 1/2 (* 1/2 (/ 1 k))))))) 1536750507.429 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- (log PI) (log (/ 1 n))) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 3)))))))) 1536750507.429 * [misc]backup-simplify: Simplify (/ (pow (* (/ 1 (- n)) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1536750507.429 * [misc]approximate: Taking taylor expansion of (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 1536750507.429 * [misc]taylor: Taking taylor expansion of (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1536750507.429 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750507.429 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in k 1536750507.429 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in k 1536750507.429 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750507.429 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750507.429 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.429 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.430 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750507.430 * [misc]taylor: Taking taylor expansion of k in k 1536750507.430 * [misc]backup-simplify: Simplify 0 into 0 1536750507.430 * [misc]backup-simplify: Simplify 1 into 1 1536750507.430 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750507.430 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.430 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.430 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in k 1536750507.430 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in k 1536750507.430 * [misc]taylor: Taking taylor expansion of -1 in k 1536750507.430 * [misc]backup-simplify: Simplify -1 into -1 1536750507.430 * [misc]taylor: Taking taylor expansion of (/ PI n) in k 1536750507.430 * [misc]taylor: Taking taylor expansion of PI in k 1536750507.430 * [misc]backup-simplify: Simplify PI into PI 1536750507.430 * [misc]taylor: Taking taylor expansion of n in k 1536750507.430 * [misc]backup-simplify: Simplify n into n 1536750507.430 * [misc]backup-simplify: Simplify (/ PI n) into (/ PI n) 1536750507.430 * [misc]backup-simplify: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 1536750507.430 * [misc]backup-simplify: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 1536750507.430 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750507.430 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750507.430 * [misc]backup-simplify: Simplify (* 1/2 (log (* -1 (/ PI n)))) into (* 1/2 (log (* -1 (/ PI n)))) 1536750507.431 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) into (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750507.431 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536750507.431 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536750507.431 * [misc]taylor: Taking taylor expansion of -1 in k 1536750507.431 * [misc]backup-simplify: Simplify -1 into -1 1536750507.431 * [misc]taylor: Taking taylor expansion of k in k 1536750507.431 * [misc]backup-simplify: Simplify 0 into 0 1536750507.431 * [misc]backup-simplify: Simplify 1 into 1 1536750507.431 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750507.431 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750507.431 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536750507.432 * [misc]backup-simplify: Simplify (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750507.432 * [misc]taylor: Taking taylor expansion of (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1536750507.432 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750507.432 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536750507.432 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536750507.432 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750507.432 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.432 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.432 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.432 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.432 * [misc]taylor: Taking taylor expansion of k in n 1536750507.432 * [misc]backup-simplify: Simplify k into k 1536750507.432 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.432 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.432 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.432 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536750507.432 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536750507.432 * [misc]taylor: Taking taylor expansion of -1 in n 1536750507.432 * [misc]backup-simplify: Simplify -1 into -1 1536750507.432 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.432 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.432 * [misc]backup-simplify: Simplify PI into PI 1536750507.432 * [misc]taylor: Taking taylor expansion of n in n 1536750507.432 * [misc]backup-simplify: Simplify 0 into 0 1536750507.432 * [misc]backup-simplify: Simplify 1 into 1 1536750507.432 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.432 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536750507.433 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536750507.433 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.433 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750507.433 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536750507.434 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536750507.434 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536750507.434 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536750507.434 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536750507.434 * [misc]taylor: Taking taylor expansion of -1 in n 1536750507.434 * [misc]backup-simplify: Simplify -1 into -1 1536750507.434 * [misc]taylor: Taking taylor expansion of k in n 1536750507.434 * [misc]backup-simplify: Simplify k into k 1536750507.434 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536750507.434 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536750507.434 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536750507.435 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536750507.435 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) 1536750507.435 * [misc]taylor: Taking taylor expansion of (/ (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 1536750507.435 * [misc]taylor: Taking taylor expansion of (pow (* -1 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750507.435 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n))))) in n 1536750507.435 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -1 (/ PI n)))) in n 1536750507.435 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750507.435 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750507.435 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.435 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.435 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750507.435 * [misc]taylor: Taking taylor expansion of k in n 1536750507.435 * [misc]backup-simplify: Simplify k into k 1536750507.435 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750507.435 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750507.435 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.435 * [misc]taylor: Taking taylor expansion of (log (* -1 (/ PI n))) in n 1536750507.435 * [misc]taylor: Taking taylor expansion of (* -1 (/ PI n)) in n 1536750507.435 * [misc]taylor: Taking taylor expansion of -1 in n 1536750507.435 * [misc]backup-simplify: Simplify -1 into -1 1536750507.435 * [misc]taylor: Taking taylor expansion of (/ PI n) in n 1536750507.435 * [misc]taylor: Taking taylor expansion of PI in n 1536750507.435 * [misc]backup-simplify: Simplify PI into PI 1536750507.435 * [misc]taylor: Taking taylor expansion of n in n 1536750507.435 * [misc]backup-simplify: Simplify 0 into 0 1536750507.436 * [misc]backup-simplify: Simplify 1 into 1 1536750507.436 * [misc]backup-simplify: Simplify (/ PI 1) into PI 1536750507.436 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536750507.436 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536750507.436 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750507.436 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750507.437 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536750507.437 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) 1536750507.438 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536750507.438 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536750507.438 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536750507.438 * [misc]taylor: Taking taylor expansion of -1 in n 1536750507.438 * [misc]backup-simplify: Simplify -1 into -1 1536750507.438 * [misc]taylor: Taking taylor expansion of k in n 1536750507.438 * [misc]backup-simplify: Simplify k into k 1536750507.438 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536750507.438 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536750507.438 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536750507.438 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536750507.439 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) 1536750507.439 * [misc]taylor: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) in k 1536750507.439 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) in k 1536750507.439 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))) in k 1536750507.439 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750507.439 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750507.439 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.439 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.439 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750507.439 * [misc]taylor: Taking taylor expansion of k in k 1536750507.439 * [misc]backup-simplify: Simplify 0 into 0 1536750507.439 * [misc]backup-simplify: Simplify 1 into 1 1536750507.439 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750507.439 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750507.439 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750507.439 * [misc]taylor: Taking taylor expansion of (- (log (* -1 PI)) (log n)) in k 1536750507.439 * [misc]taylor: Taking taylor expansion of (log (* -1 PI)) in k 1536750507.439 * [misc]taylor: Taking taylor expansion of (* -1 PI) in k 1536750507.439 * [misc]taylor: Taking taylor expansion of -1 in k 1536750507.439 * [misc]backup-simplify: Simplify -1 into -1 1536750507.439 * [misc]taylor: Taking taylor expansion of PI in k 1536750507.439 * [misc]backup-simplify: Simplify PI into PI 1536750507.439 * [misc]backup-simplify: Simplify (* -1 PI) into (* -1 PI) 1536750507.440 * [misc]backup-simplify: Simplify (log (* -1 PI)) into (log (* -1 PI)) 1536750507.440 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750507.440 * [misc]taylor: Taking taylor expansion of n in k 1536750507.440 * [misc]backup-simplify: Simplify n into n 1536750507.440 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750507.440 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750507.440 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750507.440 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536750507.440 * [misc]backup-simplify: Simplify (+ (log (* -1 PI)) (- (log n))) into (- (log (* -1 PI)) (log n)) 1536750507.441 * [misc]backup-simplify: Simplify (* 1/2 (- (log (* -1 PI)) (log n))) into (* 1/2 (- (log (* -1 PI)) (log n))) 1536750507.441 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) 1536750507.441 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536750507.441 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536750507.441 * [misc]taylor: Taking taylor expansion of -1 in k 1536750507.441 * [misc]backup-simplify: Simplify -1 into -1 1536750507.441 * [misc]taylor: Taking taylor expansion of k in k 1536750507.441 * [misc]backup-simplify: Simplify 0 into 0 1536750507.441 * [misc]backup-simplify: Simplify 1 into 1 1536750507.441 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750507.442 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750507.442 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536750507.442 * [misc]backup-simplify: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) 1536750507.443 * [misc]backup-simplify: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) 1536750507.444 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1536750507.444 * [misc]backup-simplify: Simplify (+ (* -1 0) (* 0 PI)) into 0 1536750507.446 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0 1536750507.446 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750507.446 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750507.446 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.447 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536750507.447 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0 1536750507.448 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750507.449 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1536750507.449 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.449 * [misc]backup-simplify: Simplify 0 into 0 1536750507.449 * [misc]backup-simplify: Simplify 0 into 0 1536750507.449 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536750507.450 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750507.450 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536750507.451 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536750507.452 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.453 * [misc]backup-simplify: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 1536750507.456 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 PI) 1)))) 2) into 0 1536750507.457 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750507.457 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750507.457 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750507.458 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 1536750507.459 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0 1536750507.461 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750507.461 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750507.462 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1536750507.463 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1536750507.463 * [misc]taylor: Taking taylor expansion of 0 in k 1536750507.463 * [misc]backup-simplify: Simplify 0 into 0 1536750507.463 * [misc]backup-simplify: Simplify 0 into 0 1536750507.463 * [misc]backup-simplify: Simplify 0 into 0 1536750507.463 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750507.464 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750507.466 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536750507.467 * [misc]backup-simplify: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -1 PI)) (log n)))))) 1536750507.470 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -1 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))))))))) 1536750507.470 * * * [misc]progress: simplifying candidates 1536750507.470 * * * * [misc]progress: [ 1 / 127 ] simplifiying candidate # 1536750507.470 * * * * [misc]progress: [ 2 / 127 ] simplifiying candidate # 1536750507.471 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1536750507.472 * * [misc]simplify: iters left: 6 (16 enodes) 1536750507.479 * * [misc]simplify: iters left: 5 (29 enodes) 1536750507.493 * * [misc]simplify: iters left: 4 (60 enodes) 1536750507.521 * * [misc]simplify: iters left: 3 (191 enodes) 1536750507.737 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k))) 1536750507.737 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k))))) 1536750507.737 * * * * [misc]progress: [ 3 / 127 ] simplifiying candidate # 1536750507.738 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1536750507.740 * * [misc]simplify: iters left: 6 (16 enodes) 1536750507.748 * * [misc]simplify: iters left: 5 (29 enodes) 1536750507.765 * * [misc]simplify: iters left: 4 (60 enodes) 1536750507.812 * * [misc]simplify: iters left: 3 (191 enodes) 1536750508.057 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k))) 1536750508.057 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k))))) 1536750508.057 * * * * [misc]progress: [ 4 / 127 ] simplifiying candidate # 1536750508.058 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k)))) 1536750508.060 * * [misc]simplify: iters left: 6 (16 enodes) 1536750508.068 * * [misc]simplify: iters left: 5 (27 enodes) 1536750508.080 * * [misc]simplify: iters left: 4 (50 enodes) 1536750508.108 * * [misc]simplify: iters left: 3 (114 enodes) 1536750508.198 * * [misc]simplify: iters left: 2 (427 enodes) 1536750508.960 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k))) 1536750508.960 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k))))) 1536750508.960 * * * * [misc]progress: [ 5 / 127 ] simplifiying candidate # 1536750508.961 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536750508.962 * * [misc]simplify: iters left: 6 (15 enodes) 1536750508.966 * * [misc]simplify: iters left: 5 (23 enodes) 1536750508.971 * * [misc]simplify: iters left: 4 (40 enodes) 1536750508.982 * * [misc]simplify: iters left: 3 (82 enodes) 1536750509.024 * * [misc]simplify: iters left: 2 (187 enodes) 1536750509.205 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k))) 1536750509.205 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k))))) 1536750509.205 * * * * [misc]progress: [ 6 / 127 ] simplifiying candidate # 1536750509.205 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1536750509.207 * * [misc]simplify: iters left: 6 (16 enodes) 1536750509.217 * * [misc]simplify: iters left: 5 (30 enodes) 1536750509.226 * * [misc]simplify: iters left: 4 (56 enodes) 1536750509.247 * * [misc]simplify: iters left: 3 (161 enodes) 1536750509.494 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k))) 1536750509.494 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k))))) 1536750509.494 * * * * [misc]progress: [ 7 / 127 ] simplifiying candidate # 1536750509.494 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k)))) 1536750509.496 * * [misc]simplify: iters left: 6 (16 enodes) 1536750509.505 * * [misc]simplify: iters left: 5 (30 enodes) 1536750509.518 * * [misc]simplify: iters left: 4 (56 enodes) 1536750509.561 * * [misc]simplify: iters left: 3 (161 enodes) 1536750509.780 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k))) 1536750509.780 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k))))) 1536750509.780 * * * * [misc]progress: [ 8 / 127 ] simplifiying candidate # 1536750509.780 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k)))) 1536750509.782 * * [misc]simplify: iters left: 6 (16 enodes) 1536750509.787 * * [misc]simplify: iters left: 5 (28 enodes) 1536750509.793 * * [misc]simplify: iters left: 4 (46 enodes) 1536750509.805 * * [misc]simplify: iters left: 3 (83 enodes) 1536750509.868 * * [misc]simplify: iters left: 2 (323 enodes) 1536750510.401 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log (* n PI)) (log 2))) (log (sqrt k))) 1536750510.401 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log (* n PI)) (log 2))) (log (sqrt k))))) 1536750510.401 * * * * [misc]progress: [ 9 / 127 ] simplifiying candidate # 1536750510.401 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (log (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536750510.402 * * [misc]simplify: iters left: 6 (15 enodes) 1536750510.406 * * [misc]simplify: iters left: 5 (24 enodes) 1536750510.411 * * [misc]simplify: iters left: 4 (36 enodes) 1536750510.419 * * [misc]simplify: iters left: 3 (60 enodes) 1536750510.448 * * [misc]simplify: iters left: 2 (163 enodes) 1536750510.702 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k))) 1536750510.702 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (log (* n PI)))) (log (sqrt k))))) 1536750510.702 * * * * [misc]progress: [ 10 / 127 ] simplifiying candidate # 1536750510.702 * * * * [misc]progress: [ 11 / 127 ] simplifiying candidate # 1536750510.702 * * * * [misc]progress: [ 12 / 127 ] simplifiying candidate # 1536750510.703 * [enter]simplify: Simplifying (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (/ (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))) 1536750510.705 * * [misc]simplify: iters left: 6 (19 enodes) 1536750510.717 * * [misc]simplify: iters left: 5 (37 enodes) 1536750510.742 * * [misc]simplify: iters left: 4 (114 enodes) 1536750510.834 * * [misc]simplify: iters left: 3 (443 enodes) 1536750511.486 * [exit]simplify: Simplified to (* (* (/ (pow (* PI n) (- 1/2 (/ k 2))) (sqrt k)) (* (pow (* PI n) (- 1/2 (/ k 2))) (pow (* PI n) (- 1/2 (/ k 2))))) (* (/ (pow 2 (- 1/2 (/ k 2))) k) (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))))) 1536750511.486 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (/ (pow (* PI n) (- 1/2 (/ k 2))) (sqrt k)) (* (pow (* PI n) (- 1/2 (/ k 2))) (pow (* PI n) (- 1/2 (/ k 2))))) (* (/ (pow 2 (- 1/2 (/ k 2))) k) (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))))))) 1536750511.486 * * * * [misc]progress: [ 13 / 127 ] simplifiying candidate # 1536750511.486 * [enter]simplify: Simplifying (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536750511.488 * * [misc]simplify: iters left: 6 (17 enodes) 1536750511.498 * * [misc]simplify: iters left: 5 (33 enodes) 1536750511.518 * * [misc]simplify: iters left: 4 (87 enodes) 1536750511.579 * * [misc]simplify: iters left: 3 (228 enodes) 1536750511.830 * [exit]simplify: Simplified to (* (/ (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* PI n) (- 1/2 (/ k 2))))) (* (/ (pow (* PI n) (- 1/2 (/ k 2))) k) (* (pow 2 (- 1/2 (/ k 2))) (pow (* PI n) (- 1/2 (/ k 2)))))) 1536750511.830 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (/ (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* PI n) (- 1/2 (/ k 2))))) (* (/ (pow (* PI n) (- 1/2 (/ k 2))) k) (* (pow 2 (- 1/2 (/ k 2))) (pow (* PI n) (- 1/2 (/ k 2)))))))) 1536750511.830 * * * * [misc]progress: [ 14 / 127 ] simplifiying candidate # 1536750511.830 * * * * [misc]progress: [ 15 / 127 ] simplifiying candidate # 1536750511.830 * * * * [misc]progress: [ 16 / 127 ] simplifiying candidate # 1536750511.830 * * * * [misc]progress: [ 17 / 127 ] simplifiying candidate # 1536750511.831 * [enter]simplify: Simplifying (* (pow 2 1/2) (pow (* n PI) (- 1/2 (/ k 2)))) 1536750511.831 * * [misc]simplify: iters left: 6 (11 enodes) 1536750511.834 * * [misc]simplify: iters left: 5 (16 enodes) 1536750511.840 * * [misc]simplify: iters left: 4 (19 enodes) 1536750511.847 * [exit]simplify: Simplified to (* (sqrt 2) (pow (* n PI) (- 1/2 (/ k 2)))) 1536750511.847 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (sqrt 2) (pow (* n PI) (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (sqrt k)))) 1536750511.847 * [enter]simplify: Simplifying (* (pow 2 (/ k 2)) (sqrt k)) 1536750511.848 * * [misc]simplify: iters left: 5 (6 enodes) 1536750511.850 * * [misc]simplify: iters left: 4 (7 enodes) 1536750511.853 * [exit]simplify: Simplified to (* (pow 2 (/ k 2)) (sqrt k)) 1536750511.853 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (sqrt 2) (pow (* n PI) (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (sqrt k)))) 1536750511.853 * * * * [misc]progress: [ 18 / 127 ] simplifiying candidate # 1536750511.853 * * * * [misc]progress: [ 19 / 127 ] simplifiying candidate # 1536750511.853 * [enter]simplify: Simplifying (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) 1536750511.854 * * [misc]simplify: iters left: 6 (12 enodes) 1536750511.858 * * [misc]simplify: iters left: 5 (15 enodes) 1536750511.860 * * [misc]simplify: iters left: 4 (18 enodes) 1536750511.863 * [exit]simplify: Simplified to (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) 1536750511.863 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (* (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536750511.863 * * * * [misc]progress: [ 20 / 127 ] simplifiying candidate # 1536750511.863 * [enter]simplify: Simplifying (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) 1536750511.864 * * [misc]simplify: iters left: 6 (12 enodes) 1536750511.866 * * [misc]simplify: iters left: 5 (15 enodes) 1536750511.868 * * [misc]simplify: iters left: 4 (18 enodes) 1536750511.871 * [exit]simplify: Simplified to (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) 1536750511.871 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536750511.871 * * * * [misc]progress: [ 21 / 127 ] simplifiying candidate # 1536750511.872 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536750511.872 * * [misc]simplify: iters left: 6 (11 enodes) 1536750511.874 * * [misc]simplify: iters left: 5 (14 enodes) 1536750511.877 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536750511.877 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))))) 1536750511.877 * * * * [misc]progress: [ 22 / 127 ] simplifiying candidate # 1536750511.877 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536750511.877 * * [misc]simplify: iters left: 6 (11 enodes) 1536750511.879 * * [misc]simplify: iters left: 5 (14 enodes) 1536750511.882 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536750511.882 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))))) 1536750511.882 * * * * [misc]progress: [ 23 / 127 ] simplifiying candidate # 1536750511.882 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt k)) 1536750511.883 * * [misc]simplify: iters left: 6 (10 enodes) 1536750511.885 * * [misc]simplify: iters left: 5 (13 enodes) 1536750511.887 * [exit]simplify: Simplified to (/ (pow (* n PI) (/ (- k) 2)) (sqrt k)) 1536750511.887 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) 1)) (/ (pow (* n PI) (/ (- k) 2)) (sqrt k)))) 1536750511.887 * * * * [misc]progress: [ 24 / 127 ] simplifiying candidate # 1536750511.887 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536750511.888 * * [misc]simplify: iters left: 6 (11 enodes) 1536750511.890 * * [misc]simplify: iters left: 5 (14 enodes) 1536750511.892 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536750511.892 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))))) 1536750511.892 * * * * [misc]progress: [ 25 / 127 ] simplifiying candidate # 1536750511.892 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536750511.893 * * [misc]simplify: iters left: 6 (11 enodes) 1536750511.895 * * [misc]simplify: iters left: 5 (14 enodes) 1536750511.899 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536750511.899 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) (sqrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))))) 1536750511.899 * * * * [misc]progress: [ 26 / 127 ] simplifiying candidate # 1536750511.899 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt k)) 1536750511.900 * * [misc]simplify: iters left: 6 (10 enodes) 1536750511.903 * * [misc]simplify: iters left: 5 (13 enodes) 1536750511.908 * [exit]simplify: Simplified to (/ (pow (* n PI) (/ (- k) 2)) (sqrt k)) 1536750511.908 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) 1/2) 1)) (/ (pow (* n PI) (/ (- k) 2)) (sqrt k)))) 1536750511.908 * * * * [misc]progress: [ 27 / 127 ] simplifiying candidate # 1536750511.908 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750511.909 * * [misc]simplify: iters left: 6 (10 enodes) 1536750511.913 * * [misc]simplify: iters left: 5 (12 enodes) 1536750511.917 * * [misc]simplify: iters left: 4 (15 enodes) 1536750511.922 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750511.922 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536750511.922 * * * * [misc]progress: [ 28 / 127 ] simplifiying candidate # 1536750511.922 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750511.923 * * [misc]simplify: iters left: 6 (10 enodes) 1536750511.927 * * [misc]simplify: iters left: 5 (12 enodes) 1536750511.931 * * [misc]simplify: iters left: 4 (15 enodes) 1536750511.936 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750511.936 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536750511.936 * * * * [misc]progress: [ 29 / 127 ] simplifiying candidate # 1536750511.936 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536750511.937 * * [misc]simplify: iters left: 6 (9 enodes) 1536750511.940 * * [misc]simplify: iters left: 5 (11 enodes) 1536750511.944 * * [misc]simplify: iters left: 4 (14 enodes) 1536750511.949 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536750511.949 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) 1)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) 1536750511.949 * * * * [misc]progress: [ 30 / 127 ] simplifiying candidate # 1536750511.949 * [enter]simplify: Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750511.950 * * [misc]simplify: iters left: 6 (13 enodes) 1536750511.954 * * [misc]simplify: iters left: 5 (16 enodes) 1536750511.959 * * [misc]simplify: iters left: 4 (19 enodes) 1536750511.962 * [exit]simplify: Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750511.962 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536750511.962 * * * * [misc]progress: [ 31 / 127 ] simplifiying candidate # 1536750511.963 * [enter]simplify: Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750511.963 * * [misc]simplify: iters left: 6 (13 enodes) 1536750511.966 * * [misc]simplify: iters left: 5 (16 enodes) 1536750511.968 * * [misc]simplify: iters left: 4 (19 enodes) 1536750511.972 * [exit]simplify: Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750511.972 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536750511.972 * * * * [misc]progress: [ 32 / 127 ] simplifiying candidate # 1536750511.972 * [enter]simplify: Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536750511.972 * * [misc]simplify: iters left: 6 (12 enodes) 1536750511.974 * * [misc]simplify: iters left: 5 (15 enodes) 1536750511.977 * * [misc]simplify: iters left: 4 (18 enodes) 1536750511.980 * [exit]simplify: Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536750511.980 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1)) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))) 1536750511.980 * * * * [misc]progress: [ 33 / 127 ] simplifiying candidate # 1536750511.980 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750511.981 * * [misc]simplify: iters left: 6 (13 enodes) 1536750511.983 * * [misc]simplify: iters left: 5 (16 enodes) 1536750511.986 * * [misc]simplify: iters left: 4 (19 enodes) 1536750511.989 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750511.989 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))) 1536750511.989 * * * * [misc]progress: [ 34 / 127 ] simplifiying candidate # 1536750511.989 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750511.990 * * [misc]simplify: iters left: 6 (13 enodes) 1536750511.992 * * [misc]simplify: iters left: 5 (16 enodes) 1536750511.995 * * [misc]simplify: iters left: 4 (19 enodes) 1536750511.999 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750511.999 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) 1536750511.999 * * * * [misc]progress: [ 35 / 127 ] simplifiying candidate # 1536750511.999 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536750512.000 * * [misc]simplify: iters left: 6 (12 enodes) 1536750512.002 * * [misc]simplify: iters left: 5 (15 enodes) 1536750512.006 * * [misc]simplify: iters left: 4 (18 enodes) 1536750512.012 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536750512.012 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1)) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)))) 1536750512.012 * * * * [misc]progress: [ 36 / 127 ] simplifiying candidate # 1536750512.012 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750512.013 * * [misc]simplify: iters left: 6 (12 enodes) 1536750512.017 * * [misc]simplify: iters left: 5 (15 enodes) 1536750512.021 * * [misc]simplify: iters left: 4 (18 enodes) 1536750512.024 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750512.024 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))))) 1536750512.024 * * * * [misc]progress: [ 37 / 127 ] simplifiying candidate # 1536750512.024 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750512.025 * * [misc]simplify: iters left: 6 (12 enodes) 1536750512.027 * * [misc]simplify: iters left: 5 (15 enodes) 1536750512.029 * * [misc]simplify: iters left: 4 (18 enodes) 1536750512.032 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750512.032 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ 1 (sqrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) 1536750512.032 * * * * [misc]progress: [ 38 / 127 ] simplifiying candidate # 1536750512.032 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536750512.033 * * [misc]simplify: iters left: 6 (11 enodes) 1536750512.035 * * [misc]simplify: iters left: 5 (14 enodes) 1536750512.037 * * [misc]simplify: iters left: 4 (17 enodes) 1536750512.040 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536750512.040 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (/ 1 1)) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536750512.040 * * * * [misc]progress: [ 39 / 127 ] simplifiying candidate # 1536750512.040 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536750512.040 * * [misc]simplify: iters left: 6 (11 enodes) 1536750512.043 * * [misc]simplify: iters left: 5 (14 enodes) 1536750512.045 * * [misc]simplify: iters left: 4 (17 enodes) 1536750512.048 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536750512.048 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) 1) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536750512.048 * * * * [misc]progress: [ 40 / 127 ] simplifiying candidate # 1536750512.048 * [enter]simplify: Simplifying (/ 1 (sqrt k)) 1536750512.048 * * [misc]simplify: iters left: 3 (4 enodes) 1536750512.049 * * [misc]simplify: iters left: 2 (6 enodes) 1536750512.050 * [exit]simplify: Simplified to (/ 1 (sqrt k)) 1536750512.050 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (/ 1 (sqrt k)))) 1536750512.050 * * * * [misc]progress: [ 41 / 127 ] simplifiying candidate # 1536750512.050 * [enter]simplify: Simplifying (pow 2 1/2) 1536750512.050 * * [misc]simplify: iters left: 1 (3 enodes) 1536750512.052 * [exit]simplify: Simplified to (sqrt 2) 1536750512.052 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt 2) (* (pow 2 (- (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536750512.052 * * * * [misc]progress: [ 42 / 127 ] simplifiying candidate # 1536750512.052 * [enter]simplify: Simplifying (pow 2 1/2) 1536750512.052 * * [misc]simplify: iters left: 1 (3 enodes) 1536750512.053 * [exit]simplify: Simplified to (sqrt 2) 1536750512.053 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt 2) (* (pow 2 (- (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536750512.053 * * * * [misc]progress: [ 43 / 127 ] simplifiying candidate # 1536750512.053 * [enter]simplify: Simplifying (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) 1536750512.054 * * [misc]simplify: iters left: 6 (8 enodes) 1536750512.055 * * [misc]simplify: iters left: 5 (10 enodes) 1536750512.057 * * [misc]simplify: iters left: 4 (13 enodes) 1536750512.059 * [exit]simplify: Simplified to (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) 1536750512.059 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536750512.059 * * * * [misc]progress: [ 44 / 127 ] simplifiying candidate # 1536750512.059 * [enter]simplify: Simplifying (sqrt (pow 2 (- 1/2 (/ k 2)))) 1536750512.060 * * [misc]simplify: iters left: 6 (7 enodes) 1536750512.061 * * [misc]simplify: iters left: 5 (9 enodes) 1536750512.062 * * [misc]simplify: iters left: 4 (12 enodes) 1536750512.064 * [exit]simplify: Simplified to (sqrt (pow 2 (- 1/2 (/ k 2)))) 1536750512.064 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536750512.064 * * * * [misc]progress: [ 45 / 127 ] simplifiying candidate # 1536750512.064 * * * * [misc]progress: [ 46 / 127 ] simplifiying candidate # 1536750512.065 * [enter]simplify: Simplifying (sqrt k) 1536750512.065 * * [misc]simplify: iters left: 1 (2 enodes) 1536750512.065 * [exit]simplify: Simplified to (sqrt k) 1536750512.065 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))) 1536750512.065 * * * * [misc]progress: [ 47 / 127 ] simplifiying candidate # 1536750512.065 * [enter]simplify: Simplifying (* (pow 2 1/2) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))) 1536750512.066 * * [misc]simplify: iters left: 6 (13 enodes) 1536750512.069 * * [misc]simplify: iters left: 5 (20 enodes) 1536750512.073 * * [misc]simplify: iters left: 4 (27 enodes) 1536750512.080 * * [misc]simplify: iters left: 3 (29 enodes) 1536750512.089 * * [misc]simplify: iters left: 2 (31 enodes) 1536750512.099 * * [misc]simplify: iters left: 1 (32 enodes) 1536750512.111 * [exit]simplify: Simplified to (* (/ (sqrt 2) (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2)))) 1536750512.111 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (/ (sqrt 2) (sqrt k)) (pow (* n PI) (- 1/2 (/ k 2)))) (pow 2 (/ k 2)))) 1536750512.111 * * * * [misc]progress: [ 48 / 127 ] simplifiying candidate # 1536750512.111 * * * * [misc]progress: [ 49 / 127 ] simplifiying candidate # 1536750512.112 * [enter]simplify: Simplifying (* (log (* n PI)) (- 1/2 (/ k 2))) 1536750512.113 * * [misc]simplify: iters left: 6 (10 enodes) 1536750512.117 * * [misc]simplify: iters left: 5 (17 enodes) 1536750512.125 * * [misc]simplify: iters left: 4 (33 enodes) 1536750512.143 * * [misc]simplify: iters left: 3 (69 enodes) 1536750512.192 * * [misc]simplify: iters left: 2 (172 enodes) 1536750512.289 * * [misc]simplify: iters left: 1 (337 enodes) 1536750512.455 * [exit]simplify: Simplified to (* (- 1/2 (/ k 2)) (log (* n PI))) 1536750512.455 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (exp (* (- 1/2 (/ k 2)) (log (* n PI)))) (sqrt k)))) 1536750512.455 * * * * [misc]progress: [ 50 / 127 ] simplifiying candidate # 1536750512.455 * * * * [misc]progress: [ 51 / 127 ] simplifiying candidate # 1536750512.455 * [enter]simplify: Simplifying (* n PI) 1536750512.456 * * [misc]simplify: iters left: 2 (3 enodes) 1536750512.457 * * [misc]simplify: iters left: 1 (4 enodes) 1536750512.459 * [exit]simplify: Simplified to (* n PI) 1536750512.459 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))) 1536750512.459 * * * * [misc]progress: [ 52 / 127 ] simplifiying candidate # 1536750512.459 * [enter]simplify: Simplifying (pow (* n PI) (/ k 2)) 1536750512.459 * * [misc]simplify: iters left: 3 (7 enodes) 1536750512.462 * * [misc]simplify: iters left: 2 (8 enodes) 1536750512.465 * [exit]simplify: Simplified to (pow (* n PI) (/ k 2)) 1536750512.465 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) 1/2) (pow (* n PI) (/ k 2))) (sqrt k)))) 1536750512.465 * * * * [misc]progress: [ 53 / 127 ] simplifiying candidate # 1536750512.466 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1536750512.466 * * [misc]simplify: iters left: 5 (6 enodes) 1536750512.468 * * [misc]simplify: iters left: 4 (8 enodes) 1536750512.471 * * [misc]simplify: iters left: 3 (11 enodes) 1536750512.475 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1536750512.475 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (pow (* n PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))) 1536750512.475 * * * * [misc]progress: [ 54 / 127 ] simplifiying candidate # 1536750512.475 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1536750512.475 * * [misc]simplify: iters left: 5 (6 enodes) 1536750512.476 * * [misc]simplify: iters left: 4 (8 enodes) 1536750512.478 * * [misc]simplify: iters left: 3 (11 enodes) 1536750512.480 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1536750512.480 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (pow (* n PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))) 1536750512.480 * * * * [misc]progress: [ 55 / 127 ] simplifiying candidate # 1536750512.480 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1536750512.480 * * [misc]simplify: iters left: 4 (5 enodes) 1536750512.481 * * [misc]simplify: iters left: 3 (7 enodes) 1536750512.482 * * [misc]simplify: iters left: 2 (10 enodes) 1536750512.484 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1536750512.484 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (pow (* n PI) 1) (- 1/2 (/ k 2))) (sqrt k)))) 1536750512.484 * * * * [misc]progress: [ 56 / 127 ] simplifiying candidate # 1536750512.484 * [enter]simplify: Simplifying (pow (* n PI) (- (/ k 2))) 1536750512.485 * * [misc]simplify: iters left: 5 (8 enodes) 1536750512.486 * * [misc]simplify: iters left: 4 (11 enodes) 1536750512.488 * [exit]simplify: Simplified to (pow (* n PI) (/ (- k) 2)) 1536750512.488 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow (* n PI) 1/2) (pow (* n PI) (/ (- k) 2))) (sqrt k)))) 1536750512.488 * * * * [misc]progress: [ 57 / 127 ] simplifiying candidate # 1536750512.488 * [enter]simplify: Simplifying (pow (* n PI) (- (/ k 2))) 1536750512.489 * * [misc]simplify: iters left: 5 (8 enodes) 1536750512.490 * * [misc]simplify: iters left: 4 (11 enodes) 1536750512.492 * [exit]simplify: Simplified to (pow (* n PI) (/ (- k) 2)) 1536750512.492 * [misc]simplify: Simplified (2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow (* n PI) 1/2) (pow (* n PI) (/ (- k) 2))) (sqrt k)))) 1536750512.492 * * * * [misc]progress: [ 58 / 127 ] simplifiying candidate # 1536750512.492 * [enter]simplify: Simplifying (pow n (- 1/2 (/ k 2))) 1536750512.492 * * [misc]simplify: iters left: 5 (7 enodes) 1536750512.494 * * [misc]simplify: iters left: 4 (9 enodes) 1536750512.495 * * [misc]simplify: iters left: 3 (12 enodes) 1536750512.497 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1536750512.497 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k)))) 1536750512.497 * * * * [misc]progress: [ 59 / 127 ] simplifiying candidate # 1536750512.497 * * * * [misc]progress: [ 60 / 127 ] simplifiying candidate # 1536750512.497 * * * * [misc]progress: [ 61 / 127 ] simplifiying candidate # 1536750512.497 * * * * [misc]progress: [ 62 / 127 ] simplifiying candidate # 1536750512.497 * * * * [misc]progress: [ 63 / 127 ] simplifiying candidate # 1536750512.497 * * * * [misc]progress: [ 64 / 127 ] simplifiying candidate # 1536750512.497 * * * * [misc]progress: [ 65 / 127 ] simplifiying candidate # 1536750512.497 * * * * [misc]progress: [ 66 / 127 ] simplifiying candidate # 1536750512.498 * * * * [misc]progress: [ 67 / 127 ] simplifiying candidate # 1536750512.498 * * * * [misc]progress: [ 68 / 127 ] simplifiying candidate # 1536750512.498 * * * * [misc]progress: [ 69 / 127 ] simplifiying candidate # 1536750512.498 * * * * [misc]progress: [ 70 / 127 ] simplifiying candidate # 1536750512.498 * * * * [misc]progress: [ 71 / 127 ] simplifiying candidate # 1536750512.498 * * * * [misc]progress: [ 72 / 127 ] simplifiying candidate # 1536750512.498 * * * * [misc]progress: [ 73 / 127 ] simplifiying candidate # 1536750512.498 * * * * [misc]progress: [ 74 / 127 ] simplifiying candidate # 1536750512.498 * * * * [misc]progress: [ 75 / 127 ] simplifiying candidate # 1536750512.498 * [enter]simplify: Simplifying (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750512.499 * * [misc]simplify: iters left: 6 (13 enodes) 1536750512.502 * * [misc]simplify: iters left: 5 (22 enodes) 1536750512.506 * * [misc]simplify: iters left: 4 (39 enodes) 1536750512.529 * * [misc]simplify: iters left: 3 (99 enodes) 1536750512.625 * * [misc]simplify: iters left: 2 (328 enodes) 1536750512.917 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k))) 1536750512.917 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k)))))) 1536750512.918 * * * * [misc]progress: [ 76 / 127 ] simplifiying candidate # 1536750512.918 * [enter]simplify: Simplifying (- (* (log (* n PI)) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750512.919 * * [misc]simplify: iters left: 6 (13 enodes) 1536750512.924 * * [misc]simplify: iters left: 5 (22 enodes) 1536750512.929 * * [misc]simplify: iters left: 4 (39 enodes) 1536750512.941 * * [misc]simplify: iters left: 3 (99 enodes) 1536750513.000 * * [misc]simplify: iters left: 2 (328 enodes) 1536750513.307 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k))) 1536750513.308 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k)))))) 1536750513.308 * * * * [misc]progress: [ 77 / 127 ] simplifiying candidate # 1536750513.309 * [enter]simplify: Simplifying (- (log (pow (* n PI) (- 1/2 (/ k 2)))) (log (sqrt k))) 1536750513.310 * * [misc]simplify: iters left: 6 (13 enodes) 1536750513.316 * * [misc]simplify: iters left: 5 (20 enodes) 1536750513.323 * * [misc]simplify: iters left: 4 (29 enodes) 1536750513.334 * * [misc]simplify: iters left: 3 (45 enodes) 1536750513.363 * * [misc]simplify: iters left: 2 (125 enodes) 1536750513.475 * * [misc]simplify: iters left: 1 (452 enodes) 1536750513.937 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k))) 1536750513.937 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (log (* n PI))) (log (sqrt k)))))) 1536750513.937 * * * * [misc]progress: [ 78 / 127 ] simplifiying candidate # 1536750513.937 * * * * [misc]progress: [ 79 / 127 ] simplifiying candidate # 1536750513.937 * * * * [misc]progress: [ 80 / 127 ] simplifiying candidate # 1536750513.937 * [enter]simplify: Simplifying (/ (* (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (pow (* n PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1536750513.938 * * [misc]simplify: iters left: 6 (15 enodes) 1536750513.942 * * [misc]simplify: iters left: 5 (27 enodes) 1536750513.949 * * [misc]simplify: iters left: 4 (56 enodes) 1536750513.962 * * [misc]simplify: iters left: 3 (104 enodes) 1536750513.996 * * [misc]simplify: iters left: 2 (175 enodes) 1536750514.095 * * [misc]simplify: iters left: 1 (287 enodes) 1536750514.300 * [exit]simplify: Simplified to (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (/ (* (sqrt k) k) (pow (* n PI) (- 1/2 (/ k 2))))) 1536750514.300 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (cbrt (/ (* (pow (* n PI) (- 1/2 (/ k 2))) (pow (* n PI) (- 1/2 (/ k 2)))) (/ (* (sqrt k) k) (pow (* n PI) (- 1/2 (/ k 2)))))))) 1536750514.300 * * * * [misc]progress: [ 81 / 127 ] simplifiying candidate # 1536750514.300 * * * * [misc]progress: [ 82 / 127 ] simplifiying candidate # 1536750514.301 * * * * [misc]progress: [ 83 / 127 ] simplifiying candidate # 1536750514.301 * * * * [misc]progress: [ 84 / 127 ] simplifiying candidate # 1536750514.301 * * * * [misc]progress: [ 85 / 127 ] simplifiying candidate # 1536750514.301 * [enter]simplify: Simplifying (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750514.301 * * [misc]simplify: iters left: 6 (10 enodes) 1536750514.304 * * [misc]simplify: iters left: 5 (14 enodes) 1536750514.306 * [exit]simplify: Simplified to (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750514.306 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))))) 1536750514.306 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536750514.307 * * [misc]simplify: iters left: 6 (11 enodes) 1536750514.309 * * [misc]simplify: iters left: 5 (14 enodes) 1536750514.311 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536750514.311 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))))) 1536750514.311 * * * * [misc]progress: [ 86 / 127 ] simplifiying candidate # 1536750514.311 * [enter]simplify: Simplifying (/ (pow (* n PI) 1/2) (sqrt (sqrt k))) 1536750514.312 * * [misc]simplify: iters left: 5 (9 enodes) 1536750514.313 * * [misc]simplify: iters left: 4 (11 enodes) 1536750514.315 * [exit]simplify: Simplified to (/ (sqrt (* n PI)) (sqrt (sqrt k))) 1536750514.315 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))) 1536750514.315 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536750514.316 * * [misc]simplify: iters left: 6 (11 enodes) 1536750514.318 * * [misc]simplify: iters left: 5 (14 enodes) 1536750514.321 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536750514.321 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))) 1536750514.321 * * * * [misc]progress: [ 87 / 127 ] simplifiying candidate # 1536750514.321 * [enter]simplify: Simplifying (/ (pow (* n PI) 1/2) 1) 1536750514.322 * * [misc]simplify: iters left: 5 (7 enodes) 1536750514.325 * * [misc]simplify: iters left: 4 (11 enodes) 1536750514.329 * * [misc]simplify: iters left: 3 (13 enodes) 1536750514.332 * [exit]simplify: Simplified to (sqrt (* n PI)) 1536750514.332 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (* n PI)) (/ (pow (* n PI) (- (/ k 2))) (sqrt k))))) 1536750514.332 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt k)) 1536750514.333 * * [misc]simplify: iters left: 6 (10 enodes) 1536750514.337 * * [misc]simplify: iters left: 5 (13 enodes) 1536750514.341 * [exit]simplify: Simplified to (/ (pow (* n PI) (/ (- k) 2)) (sqrt k)) 1536750514.341 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (* n PI)) (/ (pow (* n PI) (/ (- k) 2)) (sqrt k))))) 1536750514.341 * * * * [misc]progress: [ 88 / 127 ] simplifiying candidate # 1536750514.342 * [enter]simplify: Simplifying (/ (pow (* n PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750514.342 * * [misc]simplify: iters left: 6 (10 enodes) 1536750514.346 * * [misc]simplify: iters left: 5 (14 enodes) 1536750514.351 * [exit]simplify: Simplified to (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750514.351 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))))) 1536750514.351 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536750514.352 * * [misc]simplify: iters left: 6 (11 enodes) 1536750514.357 * * [misc]simplify: iters left: 5 (14 enodes) 1536750514.362 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k))) 1536750514.362 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- (/ k 2))) (cbrt (sqrt k)))))) 1536750514.362 * * * * [misc]progress: [ 89 / 127 ] simplifiying candidate # 1536750514.362 * [enter]simplify: Simplifying (/ (pow (* n PI) 1/2) (sqrt (sqrt k))) 1536750514.363 * * [misc]simplify: iters left: 5 (9 enodes) 1536750514.366 * * [misc]simplify: iters left: 4 (11 enodes) 1536750514.370 * [exit]simplify: Simplified to (/ (sqrt (* n PI)) (sqrt (sqrt k))) 1536750514.370 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))) 1536750514.370 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536750514.371 * * [misc]simplify: iters left: 6 (11 enodes) 1536750514.375 * * [misc]simplify: iters left: 5 (14 enodes) 1536750514.380 * [exit]simplify: Simplified to (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k))) 1536750514.380 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (* n PI)) (sqrt (sqrt k))) (/ (pow (* n PI) (- (/ k 2))) (sqrt (sqrt k)))))) 1536750514.380 * * * * [misc]progress: [ 90 / 127 ] simplifiying candidate # 1536750514.381 * [enter]simplify: Simplifying (/ (pow (* n PI) 1/2) 1) 1536750514.381 * * [misc]simplify: iters left: 5 (7 enodes) 1536750514.384 * * [misc]simplify: iters left: 4 (11 enodes) 1536750514.386 * * [misc]simplify: iters left: 3 (13 enodes) 1536750514.387 * [exit]simplify: Simplified to (sqrt (* n PI)) 1536750514.387 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (* n PI)) (/ (pow (* n PI) (- (/ k 2))) (sqrt k))))) 1536750514.387 * [enter]simplify: Simplifying (/ (pow (* n PI) (- (/ k 2))) (sqrt k)) 1536750514.388 * * [misc]simplify: iters left: 6 (10 enodes) 1536750514.390 * * [misc]simplify: iters left: 5 (13 enodes) 1536750514.392 * [exit]simplify: Simplified to (/ (pow (* n PI) (/ (- k) 2)) (sqrt k)) 1536750514.392 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (* n PI)) (/ (pow (* n PI) (/ (- k) 2)) (sqrt k))))) 1536750514.392 * * * * [misc]progress: [ 91 / 127 ] simplifiying candidate # 1536750514.392 * [enter]simplify: Simplifying (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750514.393 * * [misc]simplify: iters left: 6 (11 enodes) 1536750514.395 * * [misc]simplify: iters left: 5 (15 enodes) 1536750514.397 * * [misc]simplify: iters left: 4 (18 enodes) 1536750514.401 * [exit]simplify: Simplified to (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750514.401 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1536750514.402 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750514.402 * * [misc]simplify: iters left: 6 (10 enodes) 1536750514.404 * * [misc]simplify: iters left: 5 (12 enodes) 1536750514.406 * * [misc]simplify: iters left: 4 (15 enodes) 1536750514.408 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750514.408 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1536750514.408 * * * * [misc]progress: [ 92 / 127 ] simplifiying candidate # 1536750514.409 * [enter]simplify: Simplifying (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750514.409 * * [misc]simplify: iters left: 6 (10 enodes) 1536750514.411 * * [misc]simplify: iters left: 5 (12 enodes) 1536750514.414 * * [misc]simplify: iters left: 4 (15 enodes) 1536750514.419 * [exit]simplify: Simplified to (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750514.419 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1536750514.419 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750514.420 * * [misc]simplify: iters left: 6 (10 enodes) 1536750514.421 * * [misc]simplify: iters left: 5 (12 enodes) 1536750514.423 * * [misc]simplify: iters left: 4 (15 enodes) 1536750514.426 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750514.426 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1536750514.426 * * * * [misc]progress: [ 93 / 127 ] simplifiying candidate # 1536750514.426 * [enter]simplify: Simplifying (/ (pow n (- 1/2 (/ k 2))) 1) 1536750514.426 * * [misc]simplify: iters left: 6 (9 enodes) 1536750514.428 * * [misc]simplify: iters left: 5 (13 enodes) 1536750514.431 * * [misc]simplify: iters left: 4 (18 enodes) 1536750514.433 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1536750514.433 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536750514.433 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536750514.434 * * [misc]simplify: iters left: 6 (9 enodes) 1536750514.435 * * [misc]simplify: iters left: 5 (11 enodes) 1536750514.437 * * [misc]simplify: iters left: 4 (14 enodes) 1536750514.439 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536750514.440 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536750514.440 * * * * [misc]progress: [ 94 / 127 ] simplifiying candidate # 1536750514.440 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750514.441 * * [misc]simplify: iters left: 6 (15 enodes) 1536750514.444 * * [misc]simplify: iters left: 5 (24 enodes) 1536750514.450 * * [misc]simplify: iters left: 4 (36 enodes) 1536750514.461 * * [misc]simplify: iters left: 3 (39 enodes) 1536750514.471 * * [misc]simplify: iters left: 2 (42 enodes) 1536750514.487 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1536750514.487 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1536750514.487 * [enter]simplify: Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750514.488 * * [misc]simplify: iters left: 6 (13 enodes) 1536750514.492 * * [misc]simplify: iters left: 5 (16 enodes) 1536750514.499 * * [misc]simplify: iters left: 4 (19 enodes) 1536750514.505 * [exit]simplify: Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750514.505 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1536750514.505 * * * * [misc]progress: [ 95 / 127 ] simplifiying candidate # 1536750514.505 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1536750514.507 * * [misc]simplify: iters left: 6 (14 enodes) 1536750514.512 * * [misc]simplify: iters left: 5 (19 enodes) 1536750514.518 * * [misc]simplify: iters left: 4 (24 enodes) 1536750514.525 * * [misc]simplify: iters left: 3 (25 enodes) 1536750514.535 * [exit]simplify: Simplified to (* (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1536750514.535 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1536750514.535 * [enter]simplify: Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750514.536 * * [misc]simplify: iters left: 6 (13 enodes) 1536750514.538 * * [misc]simplify: iters left: 5 (16 enodes) 1536750514.541 * * [misc]simplify: iters left: 4 (19 enodes) 1536750514.544 * [exit]simplify: Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750514.544 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1536750514.544 * * * * [misc]progress: [ 96 / 127 ] simplifiying candidate # 1536750514.545 * [enter]simplify: Simplifying (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1) 1536750514.545 * * [misc]simplify: iters left: 6 (13 enodes) 1536750514.548 * * [misc]simplify: iters left: 5 (20 enodes) 1536750514.552 * * [misc]simplify: iters left: 4 (29 enodes) 1536750514.556 * * [misc]simplify: iters left: 3 (31 enodes) 1536750514.559 * * [misc]simplify: iters left: 2 (36 enodes) 1536750514.565 * [exit]simplify: Simplified to (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1536750514.565 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))) 1536750514.565 * [enter]simplify: Simplifying (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536750514.566 * * [misc]simplify: iters left: 6 (12 enodes) 1536750514.568 * * [misc]simplify: iters left: 5 (15 enodes) 1536750514.573 * * [misc]simplify: iters left: 4 (18 enodes) 1536750514.579 * [exit]simplify: Simplified to (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536750514.579 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (/ (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))) 1536750514.579 * * * * [misc]progress: [ 97 / 127 ] simplifiying candidate # 1536750514.580 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750514.581 * * [misc]simplify: iters left: 6 (14 enodes) 1536750514.585 * * [misc]simplify: iters left: 5 (19 enodes) 1536750514.588 * * [misc]simplify: iters left: 4 (22 enodes) 1536750514.592 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750514.592 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1536750514.592 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750514.594 * * [misc]simplify: iters left: 6 (13 enodes) 1536750514.596 * * [misc]simplify: iters left: 5 (16 enodes) 1536750514.598 * * [misc]simplify: iters left: 4 (19 enodes) 1536750514.602 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750514.602 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1536750514.602 * * * * [misc]progress: [ 98 / 127 ] simplifiying candidate # 1536750514.602 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750514.603 * * [misc]simplify: iters left: 6 (13 enodes) 1536750514.605 * * [misc]simplify: iters left: 5 (16 enodes) 1536750514.607 * * [misc]simplify: iters left: 4 (19 enodes) 1536750514.610 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750514.610 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1536750514.611 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750514.611 * * [misc]simplify: iters left: 6 (13 enodes) 1536750514.616 * * [misc]simplify: iters left: 5 (16 enodes) 1536750514.621 * * [misc]simplify: iters left: 4 (19 enodes) 1536750514.628 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750514.628 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1536750514.628 * * * * [misc]progress: [ 99 / 127 ] simplifiying candidate # 1536750514.628 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1) 1536750514.629 * * [misc]simplify: iters left: 6 (12 enodes) 1536750514.633 * * [misc]simplify: iters left: 5 (17 enodes) 1536750514.639 * * [misc]simplify: iters left: 4 (22 enodes) 1536750514.645 * [exit]simplify: Simplified to (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1536750514.645 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))) 1536750514.646 * [enter]simplify: Simplifying (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536750514.647 * * [misc]simplify: iters left: 6 (12 enodes) 1536750514.651 * * [misc]simplify: iters left: 5 (15 enodes) 1536750514.655 * * [misc]simplify: iters left: 4 (18 enodes) 1536750514.661 * [exit]simplify: Simplified to (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k)) 1536750514.661 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (sqrt k))))) 1536750514.661 * * * * [misc]progress: [ 100 / 127 ] simplifiying candidate # 1536750514.662 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750514.662 * * [misc]simplify: iters left: 6 (6 enodes) 1536750514.665 * * [misc]simplify: iters left: 5 (10 enodes) 1536750514.668 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1536750514.668 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1536750514.669 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750514.670 * * [misc]simplify: iters left: 6 (12 enodes) 1536750514.673 * * [misc]simplify: iters left: 5 (15 enodes) 1536750514.675 * * [misc]simplify: iters left: 4 (18 enodes) 1536750514.678 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750514.678 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1536750514.678 * * * * [misc]progress: [ 101 / 127 ] simplifiying candidate # 1536750514.678 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1536750514.679 * * [misc]simplify: iters left: 4 (5 enodes) 1536750514.679 * * [misc]simplify: iters left: 3 (7 enodes) 1536750514.680 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1536750514.680 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1536750514.681 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750514.681 * * [misc]simplify: iters left: 6 (12 enodes) 1536750514.683 * * [misc]simplify: iters left: 5 (15 enodes) 1536750514.686 * * [misc]simplify: iters left: 4 (18 enodes) 1536750514.688 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750514.688 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1536750514.688 * * * * [misc]progress: [ 102 / 127 ] simplifiying candidate # 1536750514.689 * [enter]simplify: Simplifying (/ 1 1) 1536750514.689 * * [misc]simplify: iters left: 2 (2 enodes) 1536750514.689 * * [misc]simplify: iters left: 1 (4 enodes) 1536750514.690 * [exit]simplify: Simplified to 1 1536750514.690 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* 1 (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536750514.690 * [enter]simplify: Simplifying (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536750514.690 * * [misc]simplify: iters left: 6 (11 enodes) 1536750514.694 * * [misc]simplify: iters left: 5 (14 enodes) 1536750514.696 * * [misc]simplify: iters left: 4 (17 enodes) 1536750514.699 * [exit]simplify: Simplified to (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)) 1536750514.699 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* 1 (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k))))) 1536750514.699 * * * * [misc]progress: [ 103 / 127 ] simplifiying candidate # 1536750514.699 * * * * [misc]progress: [ 104 / 127 ] simplifiying candidate # 1536750514.699 * * * * [misc]progress: [ 105 / 127 ] simplifiying candidate # 1536750514.699 * * * * [misc]progress: [ 106 / 127 ] simplifiying candidate # 1536750514.699 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1536750514.699 * * [misc]simplify: iters left: 2 (3 enodes) 1536750514.700 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1536750514.700 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))) 1536750514.700 * * * * [misc]progress: [ 107 / 127 ] simplifiying candidate # 1536750514.700 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1536750514.700 * * [misc]simplify: iters left: 2 (3 enodes) 1536750514.701 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1536750514.701 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))) 1536750514.701 * * * * [misc]progress: [ 108 / 127 ] simplifiying candidate # 1536750514.701 * [enter]simplify: Simplifying (sqrt k) 1536750514.701 * * [misc]simplify: iters left: 1 (2 enodes) 1536750514.701 * [exit]simplify: Simplified to (sqrt k) 1536750514.701 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (/ (pow (* n PI) (- 1/2 (/ k 2))) 1) (sqrt k)))) 1536750514.701 * * * * [misc]progress: [ 109 / 127 ] simplifiying candidate # 1536750514.702 * [enter]simplify: Simplifying (pow (* n PI) 1/2) 1536750514.702 * * [misc]simplify: iters left: 3 (5 enodes) 1536750514.703 * * [misc]simplify: iters left: 2 (7 enodes) 1536750514.704 * [exit]simplify: Simplified to (sqrt (* n PI)) 1536750514.704 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (* n PI)) (/ (sqrt k) (pow (* n PI) (- (/ k 2))))))) 1536750514.704 * * * * [misc]progress: [ 110 / 127 ] simplifiying candidate # 1536750514.704 * [enter]simplify: Simplifying (pow (* n PI) 1/2) 1536750514.704 * * [misc]simplify: iters left: 3 (5 enodes) 1536750514.705 * * [misc]simplify: iters left: 2 (7 enodes) 1536750514.706 * [exit]simplify: Simplified to (sqrt (* n PI)) 1536750514.706 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (* n PI)) (/ (sqrt k) (pow (* n PI) (- (/ k 2))))))) 1536750514.706 * * * * [misc]progress: [ 111 / 127 ] simplifiying candidate # 1536750514.707 * [enter]simplify: Simplifying (pow n (- 1/2 (/ k 2))) 1536750514.707 * * [misc]simplify: iters left: 5 (7 enodes) 1536750514.708 * * [misc]simplify: iters left: 4 (9 enodes) 1536750514.710 * * [misc]simplify: iters left: 3 (12 enodes) 1536750514.712 * [exit]simplify: Simplified to (pow n (- 1/2 (/ k 2))) 1536750514.712 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))))) 1536750514.712 * * * * [misc]progress: [ 112 / 127 ] simplifiying candidate # 1536750514.712 * [enter]simplify: Simplifying (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1536750514.713 * * [misc]simplify: iters left: 6 (11 enodes) 1536750514.718 * * [misc]simplify: iters left: 5 (14 enodes) 1536750514.722 * * [misc]simplify: iters left: 4 (17 enodes) 1536750514.728 * [exit]simplify: Simplified to (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) 1536750514.728 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (cbrt (pow (* n PI) (- 1/2 (/ k 2)))) (cbrt (pow (* n PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* n PI) (- 1/2 (/ k 2)))))))) 1536750514.728 * * * * [misc]progress: [ 113 / 127 ] simplifiying candidate # 1536750514.729 * [enter]simplify: Simplifying (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1536750514.729 * * [misc]simplify: iters left: 6 (10 enodes) 1536750514.733 * * [misc]simplify: iters left: 5 (13 enodes) 1536750514.737 * * [misc]simplify: iters left: 4 (16 enodes) 1536750514.743 * [exit]simplify: Simplified to (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) 1536750514.743 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (pow (* n PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n PI) (- 1/2 (/ k 2)))))))) 1536750514.743 * * * * [misc]progress: [ 114 / 127 ] simplifiying candidate # 1536750514.743 * * * * [misc]progress: [ 115 / 127 ] simplifiying candidate # 1536750514.743 * [enter]simplify: Simplifying (pow (* n PI) 1/2) 1536750514.744 * * [misc]simplify: iters left: 3 (5 enodes) 1536750514.746 * * [misc]simplify: iters left: 2 (7 enodes) 1536750514.747 * [exit]simplify: Simplified to (sqrt (* n PI)) 1536750514.748 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (sqrt (* n PI)) (* (sqrt k) (pow (* n PI) (/ k 2)))))) 1536750514.748 * * * * [misc]progress: [ 116 / 127 ] simplifiying candidate # 1536750514.748 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 1536750514.748 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536750514.748 * * * * [misc]progress: [ 117 / 127 ] simplifiying candidate # 1536750514.748 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 3)))))))) 1536750514.748 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536750514.748 * * * * [misc]progress: [ 118 / 127 ] simplifiying candidate # 1536750514.748 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (* (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (exp (* (log 2) (- 1/2 (* 1/2 k))))))))))) 1536750514.748 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536750514.748 * * * * [misc]progress: [ 119 / 127 ] simplifiying candidate # 1536750514.748 * [enter]simplify: Simplifying (- (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 1/4 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (exp (* 1/2 (+ (log PI) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (* 1/2 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))))) 1536750514.751 * * [misc]simplify: iters left: 6 (36 enodes) 1536750514.763 * * [misc]simplify: iters left: 5 (100 enodes) 1536750514.816 * * [misc]simplify: iters left: 4 (302 enodes) 1536750515.180 * [exit]simplify: Simplified to (+ (- (* (* k (* k 1/8)) (* (* (pow n 1/2) (pow PI 1/2)) (* (log PI) (log PI)))) (* (* (* (pow n 1/2) (pow PI 1/2)) (* k 1/2)) (+ (log PI) (log n)))) (+ (* (pow n 1/2) (pow PI 1/2)) (* (* (pow n 1/2) (pow PI 1/2)) (+ (* (* (* k k) (log n)) (* (log n) 1/8)) (* (* 1/4 (log PI)) (* (* k k) (log n))))))) 1536750515.180 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (+ (- (* (* k (* k 1/8)) (* (* (pow n 1/2) (pow PI 1/2)) (* (log PI) (log PI)))) (* (* (* (pow n 1/2) (pow PI 1/2)) (* k 1/2)) (+ (log PI) (log n)))) (+ (* (pow n 1/2) (pow PI 1/2)) (* (* (pow n 1/2) (pow PI 1/2)) (+ (* (* (* k k) (log n)) (* (log n) 1/8)) (* (* 1/4 (log PI)) (* (* k k) (log n))))))) (sqrt k)))) 1536750515.180 * * * * [misc]progress: [ 120 / 127 ] simplifiying candidate # 1536750515.180 * [enter]simplify: Simplifying (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) 1536750515.181 * * [misc]simplify: iters left: 6 (13 enodes) 1536750515.185 * * [misc]simplify: iters left: 5 (27 enodes) 1536750515.191 * * [misc]simplify: iters left: 4 (53 enodes) 1536750515.212 * * [misc]simplify: iters left: 3 (120 enodes) 1536750515.280 * * [misc]simplify: iters left: 2 (377 enodes) 1536750515.634 * [exit]simplify: Simplified to (pow (* n PI) (- 1/2 (* 1/2 k))) 1536750515.634 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (* 1/2 k))) (sqrt k)))) 1536750515.634 * * * * [misc]progress: [ 121 / 127 ] simplifiying candidate # 1536750515.634 * [enter]simplify: Simplifying (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) 1536750515.635 * * [misc]simplify: iters left: 6 (14 enodes) 1536750515.639 * * [misc]simplify: iters left: 5 (29 enodes) 1536750515.647 * * [misc]simplify: iters left: 4 (64 enodes) 1536750515.676 * * [misc]simplify: iters left: 3 (204 enodes) 1536750515.908 * [exit]simplify: Simplified to (pow (* (* PI 1) n) (- 1/2 (* k 1/2))) 1536750515.908 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* (* PI 1) n) (- 1/2 (* k 1/2))) (sqrt k)))) 1536750515.908 * * * * [misc]progress: [ 122 / 127 ] simplifiying candidate # 1536750515.908 * [enter]simplify: Simplifying (* n PI) 1536750515.909 * * [misc]simplify: iters left: 2 (3 enodes) 1536750515.910 * * [misc]simplify: iters left: 1 (4 enodes) 1536750515.911 * [exit]simplify: Simplified to (* n PI) 1536750515.911 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536750515.911 * * * * [misc]progress: [ 123 / 127 ] simplifiying candidate # 1536750515.912 * [enter]simplify: Simplifying (* n PI) 1536750515.912 * * [misc]simplify: iters left: 2 (3 enodes) 1536750515.913 * * [misc]simplify: iters left: 1 (4 enodes) 1536750515.914 * [exit]simplify: Simplified to (* n PI) 1536750515.914 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536750515.914 * * * * [misc]progress: [ 124 / 127 ] simplifiying candidate # 1536750515.915 * [enter]simplify: Simplifying (* n PI) 1536750515.915 * * [misc]simplify: iters left: 2 (3 enodes) 1536750515.916 * * [misc]simplify: iters left: 1 (4 enodes) 1536750515.917 * [exit]simplify: Simplified to (* n PI) 1536750515.917 * [misc]simplify: Simplified (2 2 1 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (pow (* n PI) (- 1/2 (/ k 2))) (sqrt k)))) 1536750515.917 * * * * [misc]progress: [ 125 / 127 ] simplifiying candidate # 1536750515.918 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) k))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log PI) (log n))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log n) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log PI) (log n)))) (* (log PI) (pow k 2))))))))))))))))))))))) 1536750515.918 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0)) 1536750515.918 * * * * [misc]progress: [ 126 / 127 ] simplifiying candidate # 1536750515.918 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log PI) (log (/ 1 n))))) (pow k 3)))))))) 1536750515.918 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0)) 1536750515.918 * * * * [misc]progress: [ 127 / 127 ] simplifiying candidate # 1536750515.918 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (exp (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1/2 (* 1/2 k)))))))))) 1536750515.918 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0)) 1536750515.918 * * * [misc]progress: adding candidates to table 1536750518.486 * * [misc]progress: iteration 4 / 4 1536750518.486 * * * [misc]progress: picking best candidate 1536750518.560 * * * * [misc]pick: Picked # 1536750518.560 * * * [misc]progress: localizing error 1536750518.596 * * * [misc]progress: generating rewritten candidates 1536750518.596 * * * * [misc]progress: [ 1 / 4 ] rewriting at (2 2 2 1) 1536750518.605 * * * * [misc]progress: [ 2 / 4 ] rewriting at (2) 1536750518.705 * * * * [misc]progress: [ 3 / 4 ] rewriting at (2 2) 1536750518.748 * * * * [misc]progress: [ 4 / 4 ] rewriting at (2 2 2) 1536750518.785 * * * [misc]progress: generating series expansions 1536750518.785 * * * * [misc]progress: [ 1 / 4 ] generating series at (2 2 2 1) 1536750518.785 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (/ k 2))) into (pow PI (- 1/2 (* 1/2 k))) 1536750518.785 * [misc]approximate: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in (k) around 0 1536750518.785 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536750518.785 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536750518.785 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536750518.785 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750518.785 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.785 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.785 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750518.785 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.785 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.785 * [misc]taylor: Taking taylor expansion of k in k 1536750518.785 * [misc]backup-simplify: Simplify 0 into 0 1536750518.785 * [misc]backup-simplify: Simplify 1 into 1 1536750518.785 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750518.785 * [misc]taylor: Taking taylor expansion of PI in k 1536750518.785 * [misc]backup-simplify: Simplify PI into PI 1536750518.786 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750518.786 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750518.786 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.786 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750518.787 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750518.787 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536750518.787 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536750518.787 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536750518.787 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536750518.787 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750518.787 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.787 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.787 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750518.787 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.787 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.787 * [misc]taylor: Taking taylor expansion of k in k 1536750518.787 * [misc]backup-simplify: Simplify 0 into 0 1536750518.787 * [misc]backup-simplify: Simplify 1 into 1 1536750518.788 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750518.788 * [misc]taylor: Taking taylor expansion of PI in k 1536750518.788 * [misc]backup-simplify: Simplify PI into PI 1536750518.788 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750518.788 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750518.788 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.788 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750518.788 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750518.789 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536750518.789 * [misc]backup-simplify: Simplify (pow PI 1/2) into (pow PI 1/2) 1536750518.791 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750518.791 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536750518.791 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750518.791 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750518.792 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 1536750518.794 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 1536750518.795 * [misc]backup-simplify: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) 1536750518.798 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536750518.798 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536750518.798 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.798 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750518.799 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 1536750518.802 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1536750518.803 * [misc]backup-simplify: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1536750518.806 * [misc]backup-simplify: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 1536750518.806 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (/ (/ 1 k) 2))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750518.806 * [misc]approximate: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 1536750518.806 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750518.806 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536750518.806 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536750518.806 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750518.806 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.806 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.807 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750518.807 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.807 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.807 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750518.807 * [misc]taylor: Taking taylor expansion of k in k 1536750518.807 * [misc]backup-simplify: Simplify 0 into 0 1536750518.807 * [misc]backup-simplify: Simplify 1 into 1 1536750518.807 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750518.807 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750518.807 * [misc]taylor: Taking taylor expansion of PI in k 1536750518.807 * [misc]backup-simplify: Simplify PI into PI 1536750518.807 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750518.807 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750518.807 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750518.807 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750518.808 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536750518.808 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750518.808 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750518.808 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536750518.808 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536750518.808 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750518.808 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.808 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.808 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750518.808 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.808 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.808 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750518.808 * [misc]taylor: Taking taylor expansion of k in k 1536750518.808 * [misc]backup-simplify: Simplify 0 into 0 1536750518.808 * [misc]backup-simplify: Simplify 1 into 1 1536750518.808 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750518.808 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750518.808 * [misc]taylor: Taking taylor expansion of PI in k 1536750518.808 * [misc]backup-simplify: Simplify PI into PI 1536750518.809 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750518.809 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750518.809 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750518.809 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750518.809 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536750518.810 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750518.810 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750518.810 * [misc]backup-simplify: Simplify 0 into 0 1536750518.810 * [misc]backup-simplify: Simplify 0 into 0 1536750518.810 * [misc]backup-simplify: Simplify 0 into 0 1536750518.810 * [misc]backup-simplify: Simplify 0 into 0 1536750518.810 * [misc]backup-simplify: Simplify 0 into 0 1536750518.810 * [misc]backup-simplify: Simplify 0 into 0 1536750518.810 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k))) 1536750518.810 * [misc]backup-simplify: Simplify (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750518.810 * [misc]approximate: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 1536750518.810 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750518.810 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536750518.810 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536750518.810 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750518.810 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750518.810 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.810 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.810 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750518.810 * [misc]taylor: Taking taylor expansion of k in k 1536750518.810 * [misc]backup-simplify: Simplify 0 into 0 1536750518.810 * [misc]backup-simplify: Simplify 1 into 1 1536750518.810 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750518.810 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.810 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.810 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750518.810 * [misc]taylor: Taking taylor expansion of PI in k 1536750518.811 * [misc]backup-simplify: Simplify PI into PI 1536750518.811 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750518.811 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750518.811 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750518.811 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750518.812 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750518.812 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750518.812 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536750518.812 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536750518.812 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750518.812 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750518.812 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.812 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.812 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750518.812 * [misc]taylor: Taking taylor expansion of k in k 1536750518.812 * [misc]backup-simplify: Simplify 0 into 0 1536750518.812 * [misc]backup-simplify: Simplify 1 into 1 1536750518.812 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750518.812 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.812 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.812 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750518.812 * [misc]taylor: Taking taylor expansion of PI in k 1536750518.812 * [misc]backup-simplify: Simplify PI into PI 1536750518.812 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750518.812 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750518.812 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750518.813 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750518.813 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750518.813 * [misc]backup-simplify: Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750518.813 * [misc]backup-simplify: Simplify 0 into 0 1536750518.813 * [misc]backup-simplify: Simplify 0 into 0 1536750518.813 * [misc]backup-simplify: Simplify 0 into 0 1536750518.813 * [misc]backup-simplify: Simplify 0 into 0 1536750518.813 * [misc]backup-simplify: Simplify 0 into 0 1536750518.813 * [misc]backup-simplify: Simplify 0 into 0 1536750518.813 * [misc]backup-simplify: Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k))) 1536750518.814 * * * * [misc]progress: [ 2 / 4 ] generating series at (2) 1536750518.814 * [misc]backup-simplify: Simplify (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) into (* (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt (/ 1 k))) 1536750518.814 * [misc]approximate: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt (/ 1 k))) in (k n) around 0 1536750518.814 * [misc]taylor: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt (/ 1 k))) in n 1536750518.814 * [misc]taylor: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in n 1536750518.814 * [misc]taylor: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 1536750518.814 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 1536750518.814 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 1536750518.814 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750518.814 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750518.814 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.814 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750518.814 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750518.814 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.814 * [misc]taylor: Taking taylor expansion of k in n 1536750518.814 * [misc]backup-simplify: Simplify k into k 1536750518.814 * [misc]taylor: Taking taylor expansion of (log n) in n 1536750518.814 * [misc]taylor: Taking taylor expansion of n in n 1536750518.814 * [misc]backup-simplify: Simplify 0 into 0 1536750518.814 * [misc]backup-simplify: Simplify 1 into 1 1536750518.814 * [misc]backup-simplify: Simplify (log 1) into 0 1536750518.815 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750518.815 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750518.815 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750518.815 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536750518.815 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 1536750518.815 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 1536750518.815 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 1536750518.815 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in n 1536750518.815 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in n 1536750518.815 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in n 1536750518.815 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750518.815 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750518.815 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.815 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750518.815 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750518.815 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.815 * [misc]taylor: Taking taylor expansion of k in n 1536750518.815 * [misc]backup-simplify: Simplify k into k 1536750518.815 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750518.815 * [misc]taylor: Taking taylor expansion of 2 in n 1536750518.815 * [misc]backup-simplify: Simplify 2 into 2 1536750518.815 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750518.815 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750518.815 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750518.816 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750518.816 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log 2)) into (* (log 2) (- 1/2 (* 1/2 k))) 1536750518.816 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 k)))) into (exp (* (log 2) (- 1/2 (* 1/2 k)))) 1536750518.816 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 1536750518.816 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 1536750518.816 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 1536750518.816 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750518.816 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750518.816 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.816 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750518.816 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750518.816 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.816 * [misc]taylor: Taking taylor expansion of k in n 1536750518.816 * [misc]backup-simplify: Simplify k into k 1536750518.816 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750518.816 * [misc]taylor: Taking taylor expansion of PI in n 1536750518.816 * [misc]backup-simplify: Simplify PI into PI 1536750518.816 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750518.816 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750518.816 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750518.816 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750518.817 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 1536750518.817 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 1536750518.817 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536750518.817 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750518.817 * [misc]taylor: Taking taylor expansion of k in n 1536750518.817 * [misc]backup-simplify: Simplify k into k 1536750518.817 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750518.817 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536750518.817 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750518.817 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536750518.817 * [misc]taylor: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt (/ 1 k))) in k 1536750518.817 * [misc]taylor: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in k 1536750518.817 * [misc]taylor: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 1536750518.817 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 1536750518.817 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 1536750518.817 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750518.817 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.817 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.817 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750518.817 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.818 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.818 * [misc]taylor: Taking taylor expansion of k in k 1536750518.818 * [misc]backup-simplify: Simplify 0 into 0 1536750518.818 * [misc]backup-simplify: Simplify 1 into 1 1536750518.818 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750518.818 * [misc]taylor: Taking taylor expansion of n in k 1536750518.818 * [misc]backup-simplify: Simplify n into n 1536750518.818 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750518.818 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750518.818 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.818 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750518.818 * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 1536750518.818 * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 1536750518.818 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 1536750518.818 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k 1536750518.818 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k 1536750518.818 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k 1536750518.818 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750518.818 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.818 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.818 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750518.818 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.818 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.818 * [misc]taylor: Taking taylor expansion of k in k 1536750518.818 * [misc]backup-simplify: Simplify 0 into 0 1536750518.818 * [misc]backup-simplify: Simplify 1 into 1 1536750518.818 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536750518.818 * [misc]taylor: Taking taylor expansion of 2 in k 1536750518.818 * [misc]backup-simplify: Simplify 2 into 2 1536750518.818 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750518.819 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750518.819 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.819 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750518.819 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536750518.819 * [misc]backup-simplify: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 1536750518.819 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536750518.819 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536750518.819 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536750518.819 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750518.819 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.819 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.819 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750518.819 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.819 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.819 * [misc]taylor: Taking taylor expansion of k in k 1536750518.820 * [misc]backup-simplify: Simplify 0 into 0 1536750518.820 * [misc]backup-simplify: Simplify 1 into 1 1536750518.820 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750518.820 * [misc]taylor: Taking taylor expansion of PI in k 1536750518.820 * [misc]backup-simplify: Simplify PI into PI 1536750518.820 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750518.820 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750518.820 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.820 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750518.821 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750518.821 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536750518.821 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536750518.821 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750518.821 * [misc]taylor: Taking taylor expansion of k in k 1536750518.821 * [misc]backup-simplify: Simplify 0 into 0 1536750518.821 * [misc]backup-simplify: Simplify 1 into 1 1536750518.821 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750518.821 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750518.822 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750518.822 * [misc]taylor: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt (/ 1 k))) in k 1536750518.822 * [misc]taylor: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in k 1536750518.822 * [misc]taylor: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 1536750518.822 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 1536750518.822 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 1536750518.822 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750518.822 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.822 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.822 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750518.822 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.822 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.822 * [misc]taylor: Taking taylor expansion of k in k 1536750518.822 * [misc]backup-simplify: Simplify 0 into 0 1536750518.822 * [misc]backup-simplify: Simplify 1 into 1 1536750518.822 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750518.822 * [misc]taylor: Taking taylor expansion of n in k 1536750518.822 * [misc]backup-simplify: Simplify n into n 1536750518.822 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750518.822 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750518.822 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.822 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750518.822 * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 1536750518.823 * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 1536750518.823 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 1536750518.823 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k 1536750518.823 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k 1536750518.823 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k 1536750518.823 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750518.823 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.823 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.823 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750518.823 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.823 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.823 * [misc]taylor: Taking taylor expansion of k in k 1536750518.823 * [misc]backup-simplify: Simplify 0 into 0 1536750518.823 * [misc]backup-simplify: Simplify 1 into 1 1536750518.823 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536750518.823 * [misc]taylor: Taking taylor expansion of 2 in k 1536750518.823 * [misc]backup-simplify: Simplify 2 into 2 1536750518.823 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750518.823 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750518.823 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.823 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750518.823 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536750518.824 * [misc]backup-simplify: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 1536750518.824 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536750518.824 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536750518.824 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536750518.824 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750518.824 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.824 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.824 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750518.824 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750518.824 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750518.824 * [misc]taylor: Taking taylor expansion of k in k 1536750518.824 * [misc]backup-simplify: Simplify 0 into 0 1536750518.824 * [misc]backup-simplify: Simplify 1 into 1 1536750518.824 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750518.824 * [misc]taylor: Taking taylor expansion of PI in k 1536750518.824 * [misc]backup-simplify: Simplify PI into PI 1536750518.824 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750518.825 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750518.825 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.825 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750518.825 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750518.826 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536750518.826 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536750518.826 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750518.826 * [misc]taylor: Taking taylor expansion of k in k 1536750518.826 * [misc]backup-simplify: Simplify 0 into 0 1536750518.826 * [misc]backup-simplify: Simplify 1 into 1 1536750518.826 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750518.826 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750518.826 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750518.827 * [misc]backup-simplify: Simplify (* (pow 2 1/2) (pow PI 1/2)) into (sqrt (* PI 2)) 1536750518.827 * [misc]backup-simplify: Simplify (* (pow n 1/2) (sqrt (* PI 2))) into (* (sqrt 2) (sqrt (* n PI))) 1536750518.828 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (sqrt (* n PI))) 0) into 0 1536750518.828 * [misc]taylor: Taking taylor expansion of 0 in n 1536750518.828 * [misc]backup-simplify: Simplify 0 into 0 1536750518.828 * [misc]backup-simplify: Simplify 0 into 0 1536750518.829 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750518.829 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536750518.830 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750518.830 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750518.830 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 1536750518.832 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 1536750518.834 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536750518.834 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536750518.834 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750518.834 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750518.835 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log 2))) into (- (* 1/2 (log 2))) 1536750518.837 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 1) 1)))) into (* -1/2 (* (log 2) (sqrt 2))) 1536750518.839 * [misc]backup-simplify: Simplify (+ (* (pow 2 1/2) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/2 (* (log 2) (sqrt 2))) (pow PI 1/2))) into (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI))))) 1536750518.840 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536750518.840 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536750518.840 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750518.840 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750518.840 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 1536750518.841 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 1536750518.844 * [misc]backup-simplify: Simplify (+ (* (pow n 1/2) (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI)))))) (* (* -1/2 (* (sqrt n) (log n))) (sqrt (* PI 2)))) into (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) 1536750518.846 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (sqrt (* n PI))) +nan.0) (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 1536750518.846 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 1536750518.846 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1536750518.846 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750518.846 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750518.846 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1536750518.846 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750518.846 * [misc]taylor: Taking taylor expansion of 2 in n 1536750518.846 * [misc]backup-simplify: Simplify 2 into 2 1536750518.846 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750518.846 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750518.846 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750518.846 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750518.846 * [misc]taylor: Taking taylor expansion of n in n 1536750518.846 * [misc]backup-simplify: Simplify 0 into 0 1536750518.846 * [misc]backup-simplify: Simplify 1 into 1 1536750518.846 * [misc]taylor: Taking taylor expansion of PI in n 1536750518.846 * [misc]backup-simplify: Simplify PI into PI 1536750518.846 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750518.847 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750518.847 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750518.847 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750518.847 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536750518.847 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750518.848 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.848 * [misc]backup-simplify: Simplify 0 into 0 1536750518.848 * [misc]backup-simplify: Simplify 0 into 0 1536750518.848 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536750518.849 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750518.852 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536750518.852 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536750518.852 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.852 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750518.853 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 1536750518.856 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1536750518.859 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 1536750518.859 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536750518.859 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.859 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750518.859 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log 2)))) into 0 1536750518.862 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log 2) 2) (sqrt 2))) 1536750518.872 * [misc]backup-simplify: Simplify (+ (* (pow 2 1/2) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* -1/2 (* (log 2) (sqrt 2))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* 1/8 (* (pow (log 2) 2) (sqrt 2))) (pow PI 1/2)))) into (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI))))) 1536750518.873 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536750518.874 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536750518.874 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.874 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750518.874 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 1536750518.875 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 1536750518.888 * [misc]backup-simplify: Simplify (+ (* (pow n 1/2) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI)))))) (+ (* (* -1/2 (* (sqrt n) (log n))) (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI)))))) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (sqrt (* PI 2))))) into (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/8 (* (sqrt (* PI n)) (* (sqrt 2) (pow (log PI) 2)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (* 1/4 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))))))))) 1536750518.898 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (sqrt (* n PI))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) +nan.0) (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/8 (* (sqrt (* PI n)) (* (sqrt 2) (pow (log PI) 2)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (* 1/4 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))))))))) 0))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))))) 1536750518.898 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))))) in n 1536750518.898 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))))) in n 1536750518.898 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n 1536750518.898 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750518.898 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750518.898 * [misc]taylor: Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n 1536750518.898 * [misc]taylor: Taking taylor expansion of (* (log 2) (sqrt 2)) in n 1536750518.898 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750518.898 * [misc]taylor: Taking taylor expansion of 2 in n 1536750518.898 * [misc]backup-simplify: Simplify 2 into 2 1536750518.898 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750518.899 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750518.899 * [misc]taylor: Taking taylor expansion of 2 in n 1536750518.899 * [misc]backup-simplify: Simplify 2 into 2 1536750518.899 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750518.899 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750518.899 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750518.899 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750518.899 * [misc]taylor: Taking taylor expansion of n in n 1536750518.899 * [misc]backup-simplify: Simplify 0 into 0 1536750518.899 * [misc]backup-simplify: Simplify 1 into 1 1536750518.899 * [misc]taylor: Taking taylor expansion of PI in n 1536750518.899 * [misc]backup-simplify: Simplify PI into PI 1536750518.899 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750518.900 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750518.900 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750518.900 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750518.900 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) in n 1536750518.900 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))) in n 1536750518.900 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n 1536750518.900 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750518.900 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750518.900 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n 1536750518.900 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 1536750518.900 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750518.900 * [misc]taylor: Taking taylor expansion of 2 in n 1536750518.900 * [misc]backup-simplify: Simplify 2 into 2 1536750518.900 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750518.900 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750518.900 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750518.900 * [misc]taylor: Taking taylor expansion of PI in n 1536750518.901 * [misc]backup-simplify: Simplify PI into PI 1536750518.901 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750518.901 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1536750518.901 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1536750518.901 * [misc]taylor: Taking taylor expansion of PI in n 1536750518.901 * [misc]backup-simplify: Simplify PI into PI 1536750518.901 * [misc]taylor: Taking taylor expansion of n in n 1536750518.901 * [misc]backup-simplify: Simplify 0 into 0 1536750518.901 * [misc]backup-simplify: Simplify 1 into 1 1536750518.901 * [misc]backup-simplify: Simplify (* PI 0) into 0 1536750518.901 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1536750518.902 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750518.902 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750518.902 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) in n 1536750518.902 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) in n 1536750518.902 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1536750518.902 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750518.902 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750518.902 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1536750518.902 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750518.902 * [misc]taylor: Taking taylor expansion of 2 in n 1536750518.902 * [misc]backup-simplify: Simplify 2 into 2 1536750518.902 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750518.902 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750518.902 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750518.902 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750518.902 * [misc]taylor: Taking taylor expansion of n in n 1536750518.902 * [misc]backup-simplify: Simplify 0 into 0 1536750518.902 * [misc]backup-simplify: Simplify 1 into 1 1536750518.902 * [misc]taylor: Taking taylor expansion of PI in n 1536750518.902 * [misc]backup-simplify: Simplify PI into PI 1536750518.903 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750518.903 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750518.903 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750518.903 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750518.903 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))) in n 1536750518.903 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) in n 1536750518.903 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750518.904 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750518.904 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log n)) (sqrt (* n PI))) in n 1536750518.904 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log n)) in n 1536750518.904 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750518.904 * [misc]taylor: Taking taylor expansion of 2 in n 1536750518.904 * [misc]backup-simplify: Simplify 2 into 2 1536750518.904 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750518.904 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750518.904 * [misc]taylor: Taking taylor expansion of (log n) in n 1536750518.904 * [misc]taylor: Taking taylor expansion of n in n 1536750518.904 * [misc]backup-simplify: Simplify 0 into 0 1536750518.904 * [misc]backup-simplify: Simplify 1 into 1 1536750518.904 * [misc]backup-simplify: Simplify (log 1) into 0 1536750518.904 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750518.904 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750518.904 * [misc]taylor: Taking taylor expansion of n in n 1536750518.904 * [misc]backup-simplify: Simplify 0 into 0 1536750518.904 * [misc]backup-simplify: Simplify 1 into 1 1536750518.904 * [misc]taylor: Taking taylor expansion of PI in n 1536750518.904 * [misc]backup-simplify: Simplify PI into PI 1536750518.904 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750518.905 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750518.905 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750518.905 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750518.905 * [misc]backup-simplify: Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2)) 1536750518.906 * [misc]backup-simplify: Simplify (* (* (log 2) (sqrt 2)) 0) into 0 1536750518.906 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750518.906 * [misc]backup-simplify: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 1536750518.907 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log PI)) 0) into 0 1536750518.907 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750518.907 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536750518.907 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750518.907 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536750518.907 * [misc]backup-simplify: Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n)) 1536750518.908 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log n)) 0) into 0 1536750518.908 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750518.908 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.908 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750518.908 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.908 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750518.908 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.908 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750518.908 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.908 * [misc]backup-simplify: Simplify 0 into 0 1536750518.909 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536750518.910 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536750518.911 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536750518.912 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 1536750518.912 * [misc]backup-simplify: Simplify 0 into 0 1536750518.912 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750518.913 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750518.918 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536750518.918 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536750518.918 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.918 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750518.919 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1536750518.924 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) 1536750518.929 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 1536750518.930 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536750518.930 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.930 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750518.931 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log 2))))) into 0 1536750518.938 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 3) 6)) (* (/ (pow (- (* 1/2 (log 2))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log 2) 3) (sqrt 2))) 1536750518.958 * [misc]backup-simplify: Simplify (+ (* (pow 2 1/2) (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* (* -1/2 (* (log 2) (sqrt 2))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* 1/8 (* (pow (log 2) 2) (sqrt 2))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/48 (* (pow (log 2) 3) (sqrt 2))) (pow PI 1/2))))) into (- (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt PI))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt PI))) (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt PI))))))) 1536750518.961 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 1536750518.962 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536750518.962 * [misc]backup-simplify: Simplify (- 0) into 0 1536750518.962 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750518.963 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log n))))) into 0 1536750518.965 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 3) 6)) (* (/ (pow (- (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt n) (pow (log n) 3))) 1536750519.025 * [misc]backup-simplify: Simplify (+ (* (pow n 1/2) (- (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt PI))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt PI))) (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt PI)))))))) (+ (* (* -1/2 (* (sqrt n) (log n))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI)))))) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI)))))) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) (sqrt (* PI 2)))))) into (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log n) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log PI) (pow (log n) 2))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt (* PI n)))) (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (log 2) (* (sqrt 2) (* (log PI) (log n)))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log PI) 2) (log n))) (sqrt (* PI n)))) (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))))))))))))) 1536750519.105 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (sqrt (* n PI))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) +nan.0) (+ (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/8 (* (sqrt (* PI n)) (* (sqrt 2) (pow (log PI) 2)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (* 1/4 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))))))))) +nan.0) (* (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log n) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log PI) (pow (log n) 2))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt (* PI n)))) (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (log 2) (* (sqrt 2) (* (log PI) (log n)))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log PI) 2) (log n))) (sqrt (* PI n)))) (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))))))))))))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))))))) 1536750519.105 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))))))) in n 1536750519.105 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))))))))) in n 1536750519.105 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) in n 1536750519.105 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.105 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.105 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI))) in n 1536750519.105 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log n) 2)) in n 1536750519.105 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750519.105 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.105 * [misc]backup-simplify: Simplify 2 into 2 1536750519.105 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750519.106 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750519.106 * [misc]taylor: Taking taylor expansion of (pow (log n) 2) in n 1536750519.106 * [misc]taylor: Taking taylor expansion of (log n) in n 1536750519.106 * [misc]taylor: Taking taylor expansion of n in n 1536750519.106 * [misc]backup-simplify: Simplify 0 into 0 1536750519.106 * [misc]backup-simplify: Simplify 1 into 1 1536750519.106 * [misc]backup-simplify: Simplify (log 1) into 0 1536750519.106 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536750519.106 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750519.106 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750519.106 * [misc]taylor: Taking taylor expansion of n in n 1536750519.106 * [misc]backup-simplify: Simplify 0 into 0 1536750519.106 * [misc]backup-simplify: Simplify 1 into 1 1536750519.106 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.106 * [misc]backup-simplify: Simplify PI into PI 1536750519.106 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750519.107 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750519.107 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.107 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750519.107 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))))) in n 1536750519.107 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))))))) in n 1536750519.107 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) in n 1536750519.107 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.107 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.107 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n))) in n 1536750519.107 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (pow (log PI) 2)) in n 1536750519.107 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750519.107 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.107 * [misc]backup-simplify: Simplify 2 into 2 1536750519.107 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750519.108 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750519.108 * [misc]taylor: Taking taylor expansion of (pow (log PI) 2) in n 1536750519.108 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.108 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.108 * [misc]backup-simplify: Simplify PI into PI 1536750519.108 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.108 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1536750519.108 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1536750519.108 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.108 * [misc]backup-simplify: Simplify PI into PI 1536750519.108 * [misc]taylor: Taking taylor expansion of n in n 1536750519.108 * [misc]backup-simplify: Simplify 0 into 0 1536750519.108 * [misc]backup-simplify: Simplify 1 into 1 1536750519.108 * [misc]backup-simplify: Simplify (* PI 0) into 0 1536750519.109 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1536750519.109 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.109 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750519.109 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))) in n 1536750519.109 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))))) in n 1536750519.109 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) in n 1536750519.109 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.109 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.109 * [misc]taylor: Taking taylor expansion of (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI))) in n 1536750519.109 * [misc]taylor: Taking taylor expansion of (* (pow (log 2) 2) (sqrt 2)) in n 1536750519.109 * [misc]taylor: Taking taylor expansion of (pow (log 2) 2) in n 1536750519.109 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750519.109 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.109 * [misc]backup-simplify: Simplify 2 into 2 1536750519.109 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.109 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750519.109 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.109 * [misc]backup-simplify: Simplify 2 into 2 1536750519.110 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750519.110 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750519.110 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750519.110 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750519.110 * [misc]taylor: Taking taylor expansion of n in n 1536750519.110 * [misc]backup-simplify: Simplify 0 into 0 1536750519.110 * [misc]backup-simplify: Simplify 1 into 1 1536750519.110 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.110 * [misc]backup-simplify: Simplify PI into PI 1536750519.110 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750519.110 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750519.111 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.111 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750519.111 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))) in n 1536750519.111 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))) in n 1536750519.111 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 1536750519.111 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.111 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.111 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 1536750519.111 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750519.111 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.111 * [misc]backup-simplify: Simplify 2 into 2 1536750519.111 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750519.111 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750519.111 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750519.111 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750519.111 * [misc]taylor: Taking taylor expansion of n in n 1536750519.111 * [misc]backup-simplify: Simplify 0 into 0 1536750519.111 * [misc]backup-simplify: Simplify 1 into 1 1536750519.111 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.111 * [misc]backup-simplify: Simplify PI into PI 1536750519.112 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750519.112 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750519.112 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.112 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750519.112 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))) in n 1536750519.112 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))) in n 1536750519.113 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) in n 1536750519.113 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.113 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.113 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log n)) (sqrt (* n PI))) in n 1536750519.113 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log n)) in n 1536750519.113 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750519.113 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.113 * [misc]backup-simplify: Simplify 2 into 2 1536750519.113 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750519.113 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750519.113 * [misc]taylor: Taking taylor expansion of (log n) in n 1536750519.113 * [misc]taylor: Taking taylor expansion of n in n 1536750519.113 * [misc]backup-simplify: Simplify 0 into 0 1536750519.113 * [misc]backup-simplify: Simplify 1 into 1 1536750519.113 * [misc]backup-simplify: Simplify (log 1) into 0 1536750519.113 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750519.113 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750519.113 * [misc]taylor: Taking taylor expansion of n in n 1536750519.113 * [misc]backup-simplify: Simplify 0 into 0 1536750519.113 * [misc]backup-simplify: Simplify 1 into 1 1536750519.113 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.113 * [misc]backup-simplify: Simplify PI into PI 1536750519.113 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750519.114 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750519.114 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.114 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750519.114 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))) in n 1536750519.114 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))) in n 1536750519.114 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n 1536750519.114 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.114 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.114 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n 1536750519.114 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 1536750519.114 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750519.114 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.114 * [misc]backup-simplify: Simplify 2 into 2 1536750519.115 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750519.115 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750519.115 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.115 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.115 * [misc]backup-simplify: Simplify PI into PI 1536750519.115 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.115 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1536750519.115 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1536750519.115 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.115 * [misc]backup-simplify: Simplify PI into PI 1536750519.115 * [misc]taylor: Taking taylor expansion of n in n 1536750519.115 * [misc]backup-simplify: Simplify 0 into 0 1536750519.115 * [misc]backup-simplify: Simplify 1 into 1 1536750519.115 * [misc]backup-simplify: Simplify (* PI 0) into 0 1536750519.116 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1536750519.116 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.116 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750519.116 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))) in n 1536750519.116 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))) in n 1536750519.116 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) in n 1536750519.116 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.116 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.116 * [misc]taylor: Taking taylor expansion of (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))) in n 1536750519.116 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (* (log PI) (log n))) in n 1536750519.116 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750519.116 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.116 * [misc]backup-simplify: Simplify 2 into 2 1536750519.116 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750519.116 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750519.117 * [misc]taylor: Taking taylor expansion of (* (log PI) (log n)) in n 1536750519.117 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.117 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.117 * [misc]backup-simplify: Simplify PI into PI 1536750519.117 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.117 * [misc]taylor: Taking taylor expansion of (log n) in n 1536750519.117 * [misc]taylor: Taking taylor expansion of n in n 1536750519.117 * [misc]backup-simplify: Simplify 0 into 0 1536750519.117 * [misc]backup-simplify: Simplify 1 into 1 1536750519.117 * [misc]backup-simplify: Simplify (log 1) into 0 1536750519.117 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1536750519.117 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1536750519.117 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.117 * [misc]backup-simplify: Simplify PI into PI 1536750519.117 * [misc]taylor: Taking taylor expansion of n in n 1536750519.117 * [misc]backup-simplify: Simplify 0 into 0 1536750519.117 * [misc]backup-simplify: Simplify 1 into 1 1536750519.117 * [misc]backup-simplify: Simplify (* PI 0) into 0 1536750519.118 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1536750519.118 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.118 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750519.118 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))) in n 1536750519.118 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))) in n 1536750519.118 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) in n 1536750519.118 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.118 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.118 * [misc]taylor: Taking taylor expansion of (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI))) in n 1536750519.118 * [misc]taylor: Taking taylor expansion of (* (log 2) (* (sqrt 2) (log n))) in n 1536750519.118 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750519.118 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.118 * [misc]backup-simplify: Simplify 2 into 2 1536750519.119 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.119 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log n)) in n 1536750519.119 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750519.119 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.119 * [misc]backup-simplify: Simplify 2 into 2 1536750519.119 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750519.119 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750519.119 * [misc]taylor: Taking taylor expansion of (log n) in n 1536750519.119 * [misc]taylor: Taking taylor expansion of n in n 1536750519.119 * [misc]backup-simplify: Simplify 0 into 0 1536750519.119 * [misc]backup-simplify: Simplify 1 into 1 1536750519.119 * [misc]backup-simplify: Simplify (log 1) into 0 1536750519.119 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750519.119 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750519.119 * [misc]taylor: Taking taylor expansion of n in n 1536750519.119 * [misc]backup-simplify: Simplify 0 into 0 1536750519.119 * [misc]backup-simplify: Simplify 1 into 1 1536750519.119 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.119 * [misc]backup-simplify: Simplify PI into PI 1536750519.119 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750519.120 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750519.120 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.120 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750519.120 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))) in n 1536750519.120 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))) in n 1536750519.120 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) in n 1536750519.120 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.120 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.120 * [misc]taylor: Taking taylor expansion of (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n))) in n 1536750519.120 * [misc]taylor: Taking taylor expansion of (* (log 2) (* (sqrt 2) (log PI))) in n 1536750519.120 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750519.120 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.120 * [misc]backup-simplify: Simplify 2 into 2 1536750519.120 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.121 * [misc]taylor: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 1536750519.121 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750519.121 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.121 * [misc]backup-simplify: Simplify 2 into 2 1536750519.121 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750519.121 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750519.121 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.121 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.121 * [misc]backup-simplify: Simplify PI into PI 1536750519.121 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.121 * [misc]taylor: Taking taylor expansion of (sqrt (* PI n)) in n 1536750519.121 * [misc]taylor: Taking taylor expansion of (* PI n) in n 1536750519.121 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.121 * [misc]backup-simplify: Simplify PI into PI 1536750519.121 * [misc]taylor: Taking taylor expansion of n in n 1536750519.121 * [misc]backup-simplify: Simplify 0 into 0 1536750519.121 * [misc]backup-simplify: Simplify 1 into 1 1536750519.121 * [misc]backup-simplify: Simplify (* PI 0) into 0 1536750519.122 * [misc]backup-simplify: Simplify (+ (* PI 1) (* 0 0)) into PI 1536750519.122 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.122 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750519.122 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))) in n 1536750519.122 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n 1536750519.122 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.122 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.122 * [misc]taylor: Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n 1536750519.122 * [misc]taylor: Taking taylor expansion of (* (log 2) (sqrt 2)) in n 1536750519.122 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750519.122 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.122 * [misc]backup-simplify: Simplify 2 into 2 1536750519.122 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.122 * [misc]taylor: Taking taylor expansion of (sqrt 2) in n 1536750519.123 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.123 * [misc]backup-simplify: Simplify 2 into 2 1536750519.123 * [misc]backup-simplify: Simplify (sqrt 2) into (sqrt 2) 1536750519.123 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt 2))) into 0 1536750519.123 * [misc]taylor: Taking taylor expansion of (sqrt (* n PI)) in n 1536750519.123 * [misc]taylor: Taking taylor expansion of (* n PI) in n 1536750519.123 * [misc]taylor: Taking taylor expansion of n in n 1536750519.123 * [misc]backup-simplify: Simplify 0 into 0 1536750519.123 * [misc]backup-simplify: Simplify 1 into 1 1536750519.123 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.123 * [misc]backup-simplify: Simplify PI into PI 1536750519.123 * [misc]backup-simplify: Simplify (* 0 PI) into 0 1536750519.124 * [misc]backup-simplify: Simplify (+ (* 0 0) (* 1 PI)) into PI 1536750519.124 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.124 * [misc]backup-simplify: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 1536750519.124 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536750519.124 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536750519.125 * [misc]backup-simplify: Simplify (* (log n) (log n)) into (pow (log n) 2) 1536750519.125 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (log n) 2)) into (* (sqrt 2) (pow (log n) 2)) 1536750519.125 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (log n) 2)) 0) into 0 1536750519.125 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750519.126 * [misc]backup-simplify: Simplify (* (log PI) (log PI)) into (pow (log PI) 2) 1536750519.127 * [misc]backup-simplify: Simplify (* (sqrt 2) (pow (log PI) 2)) into (* (sqrt 2) (pow (log PI) 2)) 1536750519.128 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (pow (log PI) 2)) 0) into 0 1536750519.128 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750519.128 * [misc]backup-simplify: Simplify (* (log 2) (log 2)) into (pow (log 2) 2) 1536750519.129 * [misc]backup-simplify: Simplify (* (pow (log 2) 2) (sqrt 2)) into (* (pow (log 2) 2) (sqrt 2)) 1536750519.130 * [misc]backup-simplify: Simplify (* (* (pow (log 2) 2) (sqrt 2)) 0) into 0 1536750519.130 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750519.130 * [misc]backup-simplify: Simplify (* (sqrt 2) 0) into 0 1536750519.130 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750519.130 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536750519.130 * [misc]backup-simplify: Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n)) 1536750519.131 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log n)) 0) into 0 1536750519.131 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750519.131 * [misc]backup-simplify: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 1536750519.132 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (log PI)) 0) into 0 1536750519.132 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750519.132 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536750519.132 * [misc]backup-simplify: Simplify (* (log PI) (log n)) into (* (log PI) (log n)) 1536750519.132 * [misc]backup-simplify: Simplify (* (sqrt 2) (* (log PI) (log n))) into (* (sqrt 2) (* (log PI) (log n))) 1536750519.133 * [misc]backup-simplify: Simplify (* (* (sqrt 2) (* (log PI) (log n))) 0) into 0 1536750519.133 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750519.133 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536750519.133 * [misc]backup-simplify: Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n)) 1536750519.133 * [misc]backup-simplify: Simplify (* (log 2) (* (sqrt 2) (log n))) into (* (log 2) (* (sqrt 2) (log n))) 1536750519.134 * [misc]backup-simplify: Simplify (* (* (log 2) (* (sqrt 2) (log n))) 0) into 0 1536750519.134 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750519.134 * [misc]backup-simplify: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 1536750519.135 * [misc]backup-simplify: Simplify (* (log 2) (* (sqrt 2) (log PI))) into (* (log 2) (* (sqrt 2) (log PI))) 1536750519.136 * [misc]backup-simplify: Simplify (* (* (log 2) (* (sqrt 2) (log PI))) 0) into 0 1536750519.136 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750519.136 * [misc]backup-simplify: Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2)) 1536750519.136 * [misc]backup-simplify: Simplify (* (* (log 2) (sqrt 2)) 0) into 0 1536750519.136 * [misc]backup-simplify: Simplify (* +nan.0 0) into 0 1536750519.137 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.137 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.137 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.137 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.137 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.137 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.137 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.137 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.137 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.137 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.138 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.138 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.138 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.138 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.138 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.138 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.138 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.138 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.138 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.138 * [misc]backup-simplify: Simplify 0 into 0 1536750519.140 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536750519.140 * [misc]backup-simplify: Simplify (+ (* (log 2) 0) (* 0 (sqrt 2))) into 0 1536750519.141 * [misc]backup-simplify: Simplify (+ (* (* (log 2) (sqrt 2)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) 1536750519.143 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) 1536750519.145 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750519.145 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (log PI))) into 0 1536750519.146 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (log PI)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) 1536750519.148 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) 1536750519.149 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536750519.150 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 1536750519.152 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1536750519.152 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536750519.152 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) 0) (* 0 (log n))) into 0 1536750519.153 * [misc]backup-simplify: Simplify (+ (* (* (sqrt 2) (log n)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log n))))) 1536750519.153 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log n))))) 1536750519.153 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) into (- (* +nan.0 (* (sqrt 2) (* PI (log n))))) 1536750519.154 * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))) 1536750519.156 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))) 1536750519.158 * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1536750519.161 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 1536750519.165 * [misc]backup-simplify: Simplify (+ (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1536750519.173 * [misc]backup-simplify: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1536750519.180 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 1536750519.182 * [misc]backup-simplify: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1536750519.184 * [misc]backup-simplify: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 1536750519.185 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 1536750519.188 * [misc]backup-simplify: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536750519.193 * [misc]backup-simplify: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536750519.195 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536750519.196 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 1536750519.203 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 1536750519.204 * [misc]backup-simplify: Simplify (* (pow 2 (- 1/2 (/ (/ 1 k) 2))) (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))))) into (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt k)) 1536750519.204 * [misc]approximate: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt k)) in (k n) around 0 1536750519.204 * [misc]taylor: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt k)) in n 1536750519.204 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1536750519.204 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.204 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in n 1536750519.204 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in n 1536750519.204 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.204 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.204 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.204 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.204 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.204 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.204 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.204 * [misc]taylor: Taking taylor expansion of k in n 1536750519.204 * [misc]backup-simplify: Simplify k into k 1536750519.204 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.204 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750519.204 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.204 * [misc]backup-simplify: Simplify 2 into 2 1536750519.204 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.204 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.204 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.205 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.205 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.205 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536750519.205 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750519.205 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.205 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1536750519.205 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1536750519.205 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.205 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.205 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.205 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.205 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.205 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.205 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.205 * [misc]taylor: Taking taylor expansion of k in n 1536750519.205 * [misc]backup-simplify: Simplify k into k 1536750519.205 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.205 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.205 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.205 * [misc]backup-simplify: Simplify PI into PI 1536750519.205 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.206 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.206 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.206 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.206 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1536750519.206 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.206 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.206 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 1536750519.206 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 1536750519.206 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.206 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.206 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.206 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.206 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.206 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.206 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.206 * [misc]taylor: Taking taylor expansion of k in n 1536750519.206 * [misc]backup-simplify: Simplify k into k 1536750519.207 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.207 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in n 1536750519.207 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n 1536750519.207 * [misc]taylor: Taking taylor expansion of n in n 1536750519.207 * [misc]backup-simplify: Simplify 0 into 0 1536750519.207 * [misc]backup-simplify: Simplify 1 into 1 1536750519.207 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.207 * [misc]backup-simplify: Simplify (log 1) into 0 1536750519.207 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.207 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.207 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.207 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536750519.207 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 1536750519.207 * [misc]backup-simplify: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 1536750519.207 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536750519.207 * [misc]taylor: Taking taylor expansion of k in n 1536750519.207 * [misc]backup-simplify: Simplify k into k 1536750519.207 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536750519.208 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536750519.208 * [misc]taylor: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt k)) in k 1536750519.208 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in k 1536750519.208 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750519.208 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k 1536750519.208 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k 1536750519.208 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750519.208 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.208 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.208 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.208 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.208 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.208 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.208 * [misc]taylor: Taking taylor expansion of k in k 1536750519.208 * [misc]backup-simplify: Simplify 0 into 0 1536750519.208 * [misc]backup-simplify: Simplify 1 into 1 1536750519.208 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.208 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536750519.208 * [misc]taylor: Taking taylor expansion of 2 in k 1536750519.208 * [misc]backup-simplify: Simplify 2 into 2 1536750519.208 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.208 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.208 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750519.208 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750519.209 * [misc]backup-simplify: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) 1536750519.211 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536750519.211 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536750519.211 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750519.211 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536750519.211 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536750519.211 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750519.211 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.211 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.211 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.211 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.211 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.211 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.211 * [misc]taylor: Taking taylor expansion of k in k 1536750519.211 * [misc]backup-simplify: Simplify 0 into 0 1536750519.211 * [misc]backup-simplify: Simplify 1 into 1 1536750519.211 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.211 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.211 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.212 * [misc]backup-simplify: Simplify PI into PI 1536750519.212 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.212 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.212 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750519.212 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750519.213 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536750519.213 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.213 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750519.213 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 1536750519.213 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 1536750519.213 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750519.213 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.213 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.213 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.213 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.213 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.213 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.213 * [misc]taylor: Taking taylor expansion of k in k 1536750519.213 * [misc]backup-simplify: Simplify 0 into 0 1536750519.213 * [misc]backup-simplify: Simplify 1 into 1 1536750519.213 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.213 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in k 1536750519.213 * [misc]taylor: Taking taylor expansion of (/ 1 n) in k 1536750519.213 * [misc]taylor: Taking taylor expansion of n in k 1536750519.213 * [misc]backup-simplify: Simplify n into n 1536750519.213 * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) 1536750519.213 * [misc]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) 1536750519.213 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.214 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750519.214 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750519.214 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 1536750519.214 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.214 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536750519.214 * [misc]taylor: Taking taylor expansion of k in k 1536750519.214 * [misc]backup-simplify: Simplify 0 into 0 1536750519.214 * [misc]backup-simplify: Simplify 1 into 1 1536750519.214 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.214 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750519.214 * [misc]taylor: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt k)) in k 1536750519.214 * [misc]taylor: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in k 1536750519.214 * [misc]taylor: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750519.214 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k 1536750519.214 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k 1536750519.214 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750519.214 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.214 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.215 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.215 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.215 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.215 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.215 * [misc]taylor: Taking taylor expansion of k in k 1536750519.215 * [misc]backup-simplify: Simplify 0 into 0 1536750519.215 * [misc]backup-simplify: Simplify 1 into 1 1536750519.215 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.215 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536750519.215 * [misc]taylor: Taking taylor expansion of 2 in k 1536750519.215 * [misc]backup-simplify: Simplify 2 into 2 1536750519.215 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.215 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.215 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750519.215 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750519.215 * [misc]backup-simplify: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) 1536750519.216 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536750519.216 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536750519.216 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750519.216 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536750519.216 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536750519.216 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750519.216 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.216 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.216 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.216 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.216 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.216 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.216 * [misc]taylor: Taking taylor expansion of k in k 1536750519.216 * [misc]backup-simplify: Simplify 0 into 0 1536750519.216 * [misc]backup-simplify: Simplify 1 into 1 1536750519.216 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.216 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.216 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.216 * [misc]backup-simplify: Simplify PI into PI 1536750519.216 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.216 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.216 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750519.217 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750519.217 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536750519.217 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.217 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750519.217 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 1536750519.217 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 1536750519.217 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750519.217 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.217 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.217 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.217 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.217 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.217 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.217 * [misc]taylor: Taking taylor expansion of k in k 1536750519.217 * [misc]backup-simplify: Simplify 0 into 0 1536750519.217 * [misc]backup-simplify: Simplify 1 into 1 1536750519.217 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.217 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in k 1536750519.218 * [misc]taylor: Taking taylor expansion of (/ 1 n) in k 1536750519.218 * [misc]taylor: Taking taylor expansion of n in k 1536750519.218 * [misc]backup-simplify: Simplify n into n 1536750519.218 * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) 1536750519.218 * [misc]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) 1536750519.218 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.218 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750519.218 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750519.218 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 1536750519.218 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.218 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536750519.218 * [misc]taylor: Taking taylor expansion of k in k 1536750519.218 * [misc]backup-simplify: Simplify 0 into 0 1536750519.218 * [misc]backup-simplify: Simplify 1 into 1 1536750519.218 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.219 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750519.219 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) 1536750519.219 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) 1536750519.220 * [misc]backup-simplify: Simplify (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) 0) into 0 1536750519.220 * [misc]taylor: Taking taylor expansion of 0 in n 1536750519.220 * [misc]backup-simplify: Simplify 0 into 0 1536750519.220 * [misc]backup-simplify: Simplify 0 into 0 1536750519.220 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) into 0 1536750519.220 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 1536750519.221 * [misc]backup-simplify: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536750519.221 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n 1536750519.221 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1536750519.221 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.221 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.221 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1536750519.221 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750519.221 * [misc]taylor: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.221 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750519.221 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.221 * [misc]backup-simplify: Simplify 2 into 2 1536750519.221 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.221 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.221 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.221 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.221 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.222 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.222 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.222 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.222 * [misc]taylor: Taking taylor expansion of k in n 1536750519.222 * [misc]backup-simplify: Simplify k into k 1536750519.222 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.222 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.222 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.222 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.222 * [misc]backup-simplify: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.222 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536750519.222 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750519.222 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.222 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1536750519.222 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1536750519.222 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.222 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.222 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.222 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.222 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.222 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.222 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.222 * [misc]taylor: Taking taylor expansion of k in n 1536750519.222 * [misc]backup-simplify: Simplify k into k 1536750519.222 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.223 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.223 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.223 * [misc]backup-simplify: Simplify PI into PI 1536750519.223 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.223 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.223 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.223 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.223 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1536750519.223 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.224 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.224 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 1536750519.224 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 1536750519.224 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.224 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.224 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.224 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.224 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.224 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.224 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.224 * [misc]taylor: Taking taylor expansion of k in n 1536750519.224 * [misc]backup-simplify: Simplify k into k 1536750519.224 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.224 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in n 1536750519.224 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n 1536750519.224 * [misc]taylor: Taking taylor expansion of n in n 1536750519.224 * [misc]backup-simplify: Simplify 0 into 0 1536750519.224 * [misc]backup-simplify: Simplify 1 into 1 1536750519.224 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.224 * [misc]backup-simplify: Simplify (log 1) into 0 1536750519.224 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.224 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.224 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.224 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536750519.224 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 1536750519.225 * [misc]backup-simplify: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 1536750519.225 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 1536750519.225 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536750519.226 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536750519.226 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 1536750519.227 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 1536750519.227 * [misc]backup-simplify: Simplify 0 into 0 1536750519.227 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750519.228 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 1536750519.228 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1536750519.229 * [misc]backup-simplify: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536750519.229 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n 1536750519.229 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1536750519.229 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.229 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.229 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1536750519.229 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750519.229 * [misc]taylor: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.229 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750519.229 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.229 * [misc]backup-simplify: Simplify 2 into 2 1536750519.229 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.229 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.229 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.229 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.229 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.229 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.229 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.229 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.229 * [misc]taylor: Taking taylor expansion of k in n 1536750519.229 * [misc]backup-simplify: Simplify k into k 1536750519.229 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.229 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.229 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.230 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.230 * [misc]backup-simplify: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.230 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536750519.230 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750519.230 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.230 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1536750519.230 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1536750519.230 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.230 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.230 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.230 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.230 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.230 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.230 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.230 * [misc]taylor: Taking taylor expansion of k in n 1536750519.230 * [misc]backup-simplify: Simplify k into k 1536750519.230 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.230 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.230 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.230 * [misc]backup-simplify: Simplify PI into PI 1536750519.230 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.230 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.231 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.231 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.231 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1536750519.231 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.231 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.231 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 1536750519.231 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 1536750519.231 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.231 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.231 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.231 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.231 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.231 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.231 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.231 * [misc]taylor: Taking taylor expansion of k in n 1536750519.231 * [misc]backup-simplify: Simplify k into k 1536750519.231 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.231 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in n 1536750519.231 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n 1536750519.231 * [misc]taylor: Taking taylor expansion of n in n 1536750519.231 * [misc]backup-simplify: Simplify 0 into 0 1536750519.231 * [misc]backup-simplify: Simplify 1 into 1 1536750519.232 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.232 * [misc]backup-simplify: Simplify (log 1) into 0 1536750519.232 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.232 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.232 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.232 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536750519.232 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 1536750519.232 * [misc]backup-simplify: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 1536750519.232 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 1536750519.233 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536750519.233 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536750519.234 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 1536750519.234 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 1536750519.234 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536750519.236 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1536750519.236 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750519.236 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750519.236 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.236 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.237 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536750519.237 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 1536750519.237 * [misc]backup-simplify: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750519.239 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750519.239 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750519.239 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750519.239 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.240 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.240 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0 1536750519.241 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750519.241 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) into 0 1536750519.241 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750519.241 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750519.241 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.241 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.243 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536750519.243 * [misc]backup-simplify: Simplify (+ (* (log 2) 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0 1536750519.244 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750519.244 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into 0 1536750519.245 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1536750519.245 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.245 * [misc]backup-simplify: Simplify 0 into 0 1536750519.245 * [misc]backup-simplify: Simplify 0 into 0 1536750519.246 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750519.246 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1536750519.247 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))))) into 0 1536750519.247 * [misc]backup-simplify: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) 1536750519.247 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n 1536750519.247 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 1536750519.248 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.248 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.248 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 1536750519.248 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750519.248 * [misc]taylor: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.248 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750519.248 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.248 * [misc]backup-simplify: Simplify 2 into 2 1536750519.248 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.248 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.248 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.248 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.248 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.248 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.248 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.248 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.248 * [misc]taylor: Taking taylor expansion of k in n 1536750519.248 * [misc]backup-simplify: Simplify k into k 1536750519.248 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.248 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.248 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.248 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.248 * [misc]backup-simplify: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.248 * [misc]backup-simplify: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 1536750519.249 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750519.249 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.249 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1536750519.249 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1536750519.249 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.249 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.249 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.249 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.249 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.249 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.249 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.249 * [misc]taylor: Taking taylor expansion of k in n 1536750519.249 * [misc]backup-simplify: Simplify k into k 1536750519.249 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.249 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.249 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.249 * [misc]backup-simplify: Simplify PI into PI 1536750519.249 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.249 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.249 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.249 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.249 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1536750519.250 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.250 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.250 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 1536750519.250 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 1536750519.250 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.250 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.250 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.250 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.250 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.250 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.250 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.250 * [misc]taylor: Taking taylor expansion of k in n 1536750519.250 * [misc]backup-simplify: Simplify k into k 1536750519.250 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.250 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in n 1536750519.250 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n 1536750519.250 * [misc]taylor: Taking taylor expansion of n in n 1536750519.250 * [misc]backup-simplify: Simplify 0 into 0 1536750519.250 * [misc]backup-simplify: Simplify 1 into 1 1536750519.250 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.250 * [misc]backup-simplify: Simplify (log 1) into 0 1536750519.250 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.250 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.250 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.251 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536750519.251 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 1536750519.251 * [misc]backup-simplify: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 1536750519.251 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 1536750519.252 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536750519.252 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536750519.253 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 1536750519.254 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 1536750519.258 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2)))))))) 1536750519.259 * [misc]backup-simplify: Simplify (* (pow 2 (- 1/2 (/ (/ 1 (- k)) 2))) (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))))) into (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) 1536750519.259 * [misc]approximate: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) in (k n) around 0 1536750519.259 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) in n 1536750519.259 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536750519.259 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.259 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 1536750519.259 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 1536750519.259 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.259 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.259 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.259 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.259 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.259 * [misc]taylor: Taking taylor expansion of k in n 1536750519.259 * [misc]backup-simplify: Simplify k into k 1536750519.259 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.259 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.259 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.259 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n 1536750519.259 * [misc]taylor: Taking taylor expansion of (/ -1 n) in n 1536750519.259 * [misc]taylor: Taking taylor expansion of -1 in n 1536750519.259 * [misc]backup-simplify: Simplify -1 into -1 1536750519.259 * [misc]taylor: Taking taylor expansion of n in n 1536750519.259 * [misc]backup-simplify: Simplify 0 into 0 1536750519.259 * [misc]backup-simplify: Simplify 1 into 1 1536750519.260 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750519.260 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536750519.260 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.260 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.260 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536750519.261 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 1536750519.261 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536750519.261 * [misc]taylor: Taking taylor expansion of (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536750519.261 * [misc]taylor: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.261 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in n 1536750519.261 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in n 1536750519.261 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.261 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.261 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.261 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.261 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.261 * [misc]taylor: Taking taylor expansion of k in n 1536750519.261 * [misc]backup-simplify: Simplify k into k 1536750519.261 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.261 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.261 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.261 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750519.262 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.262 * [misc]backup-simplify: Simplify 2 into 2 1536750519.262 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.262 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.262 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.262 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.262 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.262 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.263 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1536750519.263 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1536750519.263 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.263 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.263 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.263 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.263 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.263 * [misc]taylor: Taking taylor expansion of k in n 1536750519.263 * [misc]backup-simplify: Simplify k into k 1536750519.263 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.263 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.263 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.263 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.263 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.263 * [misc]backup-simplify: Simplify PI into PI 1536750519.263 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.264 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.264 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.264 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1536750519.264 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.264 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536750519.264 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536750519.265 * [misc]taylor: Taking taylor expansion of -1 in n 1536750519.265 * [misc]backup-simplify: Simplify -1 into -1 1536750519.265 * [misc]taylor: Taking taylor expansion of k in n 1536750519.265 * [misc]backup-simplify: Simplify k into k 1536750519.265 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536750519.265 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536750519.265 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536750519.265 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536750519.266 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.267 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750519.268 * [misc]backup-simplify: Simplify (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) into (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) 1536750519.268 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) in k 1536750519.268 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in k 1536750519.268 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750519.268 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 1536750519.268 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 1536750519.268 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750519.268 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.268 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.268 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.268 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.268 * [misc]taylor: Taking taylor expansion of k in k 1536750519.268 * [misc]backup-simplify: Simplify 0 into 0 1536750519.268 * [misc]backup-simplify: Simplify 1 into 1 1536750519.268 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.268 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.268 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.268 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in k 1536750519.268 * [misc]taylor: Taking taylor expansion of (/ -1 n) in k 1536750519.268 * [misc]taylor: Taking taylor expansion of -1 in k 1536750519.268 * [misc]backup-simplify: Simplify -1 into -1 1536750519.268 * [misc]taylor: Taking taylor expansion of n in k 1536750519.268 * [misc]backup-simplify: Simplify n into n 1536750519.269 * [misc]backup-simplify: Simplify (/ -1 n) into (/ -1 n) 1536750519.269 * [misc]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) 1536750519.269 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.269 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.269 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 1536750519.269 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.269 * [misc]taylor: Taking taylor expansion of (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 1536750519.269 * [misc]taylor: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750519.269 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k 1536750519.269 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k 1536750519.269 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750519.269 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.269 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.269 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.270 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.270 * [misc]taylor: Taking taylor expansion of k in k 1536750519.270 * [misc]backup-simplify: Simplify 0 into 0 1536750519.270 * [misc]backup-simplify: Simplify 1 into 1 1536750519.270 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.270 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.270 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.270 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536750519.270 * [misc]taylor: Taking taylor expansion of 2 in k 1536750519.270 * [misc]backup-simplify: Simplify 2 into 2 1536750519.270 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.270 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.270 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.271 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536750519.271 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.271 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750519.271 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536750519.271 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536750519.271 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750519.271 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.271 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.271 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.271 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.271 * [misc]taylor: Taking taylor expansion of k in k 1536750519.271 * [misc]backup-simplify: Simplify 0 into 0 1536750519.271 * [misc]backup-simplify: Simplify 1 into 1 1536750519.272 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.272 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.272 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.272 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.272 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.272 * [misc]backup-simplify: Simplify PI into PI 1536750519.272 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.272 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.273 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.273 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750519.274 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.274 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536750519.274 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536750519.274 * [misc]taylor: Taking taylor expansion of -1 in k 1536750519.274 * [misc]backup-simplify: Simplify -1 into -1 1536750519.274 * [misc]taylor: Taking taylor expansion of k in k 1536750519.274 * [misc]backup-simplify: Simplify 0 into 0 1536750519.274 * [misc]backup-simplify: Simplify 1 into 1 1536750519.274 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750519.274 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.275 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536750519.275 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.276 * [misc]backup-simplify: Simplify (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750519.276 * [misc]backup-simplify: Simplify (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) +nan.0) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536750519.276 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) in k 1536750519.277 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in k 1536750519.277 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750519.277 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 1536750519.277 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 1536750519.277 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750519.277 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.277 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.277 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.277 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.277 * [misc]taylor: Taking taylor expansion of k in k 1536750519.277 * [misc]backup-simplify: Simplify 0 into 0 1536750519.277 * [misc]backup-simplify: Simplify 1 into 1 1536750519.277 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.277 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.277 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.277 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in k 1536750519.277 * [misc]taylor: Taking taylor expansion of (/ -1 n) in k 1536750519.277 * [misc]taylor: Taking taylor expansion of -1 in k 1536750519.277 * [misc]backup-simplify: Simplify -1 into -1 1536750519.277 * [misc]taylor: Taking taylor expansion of n in k 1536750519.277 * [misc]backup-simplify: Simplify n into n 1536750519.277 * [misc]backup-simplify: Simplify (/ -1 n) into (/ -1 n) 1536750519.277 * [misc]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) 1536750519.278 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.278 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.278 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 1536750519.278 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.278 * [misc]taylor: Taking taylor expansion of (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 1536750519.278 * [misc]taylor: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750519.278 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k 1536750519.278 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k 1536750519.278 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750519.278 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.278 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.278 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.278 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.278 * [misc]taylor: Taking taylor expansion of k in k 1536750519.278 * [misc]backup-simplify: Simplify 0 into 0 1536750519.278 * [misc]backup-simplify: Simplify 1 into 1 1536750519.279 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.279 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.279 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.279 * [misc]taylor: Taking taylor expansion of (log 2) in k 1536750519.279 * [misc]taylor: Taking taylor expansion of 2 in k 1536750519.279 * [misc]backup-simplify: Simplify 2 into 2 1536750519.279 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.279 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.279 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.280 * [misc]backup-simplify: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 1536750519.280 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.280 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750519.280 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536750519.280 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536750519.280 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750519.280 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.280 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.280 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.280 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.280 * [misc]taylor: Taking taylor expansion of k in k 1536750519.280 * [misc]backup-simplify: Simplify 0 into 0 1536750519.280 * [misc]backup-simplify: Simplify 1 into 1 1536750519.280 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.280 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.280 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.280 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.281 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.281 * [misc]backup-simplify: Simplify PI into PI 1536750519.281 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.281 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.281 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.282 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750519.282 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.282 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536750519.282 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536750519.282 * [misc]taylor: Taking taylor expansion of -1 in k 1536750519.282 * [misc]backup-simplify: Simplify -1 into -1 1536750519.282 * [misc]taylor: Taking taylor expansion of k in k 1536750519.282 * [misc]backup-simplify: Simplify 0 into 0 1536750519.282 * [misc]backup-simplify: Simplify 1 into 1 1536750519.283 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750519.283 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.283 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536750519.284 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.284 * [misc]backup-simplify: Simplify (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750519.285 * [misc]backup-simplify: Simplify (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) +nan.0) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536750519.285 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1536750519.285 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.285 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.285 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536750519.285 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536750519.285 * [misc]taylor: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.285 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750519.285 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.285 * [misc]backup-simplify: Simplify 2 into 2 1536750519.286 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.286 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.286 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.286 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.286 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.286 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.286 * [misc]taylor: Taking taylor expansion of k in n 1536750519.286 * [misc]backup-simplify: Simplify k into k 1536750519.286 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.286 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.286 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.286 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.286 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.286 * [misc]backup-simplify: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.287 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.287 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536750519.287 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.287 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 1536750519.287 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 1536750519.287 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.287 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.287 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.287 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.287 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.287 * [misc]taylor: Taking taylor expansion of k in n 1536750519.287 * [misc]backup-simplify: Simplify k into k 1536750519.287 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.287 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.287 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.287 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n 1536750519.287 * [misc]taylor: Taking taylor expansion of (/ -1 n) in n 1536750519.287 * [misc]taylor: Taking taylor expansion of -1 in n 1536750519.287 * [misc]backup-simplify: Simplify -1 into -1 1536750519.287 * [misc]taylor: Taking taylor expansion of n in n 1536750519.287 * [misc]backup-simplify: Simplify 0 into 0 1536750519.287 * [misc]backup-simplify: Simplify 1 into 1 1536750519.288 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750519.288 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536750519.288 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.288 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.288 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536750519.289 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 1536750519.289 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536750519.289 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.289 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1536750519.289 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1536750519.289 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.289 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.289 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.289 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.289 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.289 * [misc]taylor: Taking taylor expansion of k in n 1536750519.289 * [misc]backup-simplify: Simplify k into k 1536750519.289 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.289 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.290 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.290 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.290 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.290 * [misc]backup-simplify: Simplify PI into PI 1536750519.290 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.290 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.290 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.291 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1536750519.291 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.291 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.292 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750519.293 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536750519.294 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536750519.295 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 1536750519.295 * [misc]backup-simplify: Simplify (+ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1536750519.296 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536750519.297 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750519.298 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536750519.298 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1536750519.298 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1536750519.298 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.298 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.298 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536750519.298 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.298 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 1536750519.298 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 1536750519.298 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.299 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.299 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.299 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.299 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.299 * [misc]taylor: Taking taylor expansion of k in n 1536750519.299 * [misc]backup-simplify: Simplify k into k 1536750519.299 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.299 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.299 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.299 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n 1536750519.299 * [misc]taylor: Taking taylor expansion of (/ -1 n) in n 1536750519.299 * [misc]taylor: Taking taylor expansion of -1 in n 1536750519.299 * [misc]backup-simplify: Simplify -1 into -1 1536750519.299 * [misc]taylor: Taking taylor expansion of n in n 1536750519.299 * [misc]backup-simplify: Simplify 0 into 0 1536750519.299 * [misc]backup-simplify: Simplify 1 into 1 1536750519.299 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750519.299 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536750519.299 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.300 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.300 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536750519.300 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 1536750519.301 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536750519.301 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536750519.301 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536750519.301 * [misc]taylor: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.301 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750519.301 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.301 * [misc]backup-simplify: Simplify 2 into 2 1536750519.301 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.301 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.301 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.301 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.301 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.301 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.301 * [misc]taylor: Taking taylor expansion of k in n 1536750519.301 * [misc]backup-simplify: Simplify k into k 1536750519.301 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.301 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.301 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.301 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.301 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.302 * [misc]backup-simplify: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.302 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.302 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.302 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1536750519.302 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1536750519.302 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.302 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.302 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.302 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.302 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.302 * [misc]taylor: Taking taylor expansion of k in n 1536750519.302 * [misc]backup-simplify: Simplify k into k 1536750519.302 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.302 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.302 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.302 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.302 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.303 * [misc]backup-simplify: Simplify PI into PI 1536750519.303 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.303 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.303 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.303 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1536750519.304 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.304 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.305 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750519.306 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536750519.307 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536750519.308 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536750519.311 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750519.311 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750519.311 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750519.311 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.312 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 1536750519.313 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750519.314 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536750519.317 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 1536750519.317 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750519.317 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750519.317 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.318 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536750519.318 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 1536750519.320 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750519.320 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 1536750519.320 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750519.321 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750519.321 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.323 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 1536750519.324 * [misc]backup-simplify: Simplify (+ (* (log 2) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 1536750519.325 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750519.326 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* 0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1536750519.327 * [misc]backup-simplify: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0 1536750519.327 * [misc]backup-simplify: Simplify 0 into 0 1536750519.328 * [misc]backup-simplify: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1536750519.328 * [misc]backup-simplify: Simplify (+ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0 1536750519.329 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750519.330 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750519.333 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) 1536750519.333 * [misc]taylor: Taking taylor expansion of (- (+ (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) in n 1536750519.333 * [misc]taylor: Taking taylor expansion of (+ (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) in n 1536750519.333 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1536750519.333 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.333 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.333 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536750519.333 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536750519.333 * [misc]taylor: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.333 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750519.333 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.333 * [misc]backup-simplify: Simplify 2 into 2 1536750519.333 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.333 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.333 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.333 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.334 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.334 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.334 * [misc]taylor: Taking taylor expansion of k in n 1536750519.334 * [misc]backup-simplify: Simplify k into k 1536750519.334 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.334 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.334 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.334 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.334 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.334 * [misc]backup-simplify: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.335 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.335 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536750519.335 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.335 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 1536750519.335 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 1536750519.335 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.335 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.335 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.335 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.335 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.335 * [misc]taylor: Taking taylor expansion of k in n 1536750519.335 * [misc]backup-simplify: Simplify k into k 1536750519.335 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.335 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.335 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.335 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n 1536750519.335 * [misc]taylor: Taking taylor expansion of (/ -1 n) in n 1536750519.335 * [misc]taylor: Taking taylor expansion of -1 in n 1536750519.335 * [misc]backup-simplify: Simplify -1 into -1 1536750519.335 * [misc]taylor: Taking taylor expansion of n in n 1536750519.335 * [misc]backup-simplify: Simplify 0 into 0 1536750519.335 * [misc]backup-simplify: Simplify 1 into 1 1536750519.335 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750519.336 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536750519.336 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.336 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.336 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536750519.337 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 1536750519.337 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536750519.337 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.337 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1536750519.337 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1536750519.337 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.337 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.337 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.337 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.337 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.337 * [misc]taylor: Taking taylor expansion of k in n 1536750519.337 * [misc]backup-simplify: Simplify k into k 1536750519.337 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.337 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.337 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.337 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.337 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.338 * [misc]backup-simplify: Simplify PI into PI 1536750519.338 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.338 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.338 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.338 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1536750519.339 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.339 * [misc]taylor: Taking taylor expansion of (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 1536750519.339 * [misc]taylor: Taking taylor expansion of (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 1536750519.339 * [misc]taylor: Taking taylor expansion of +nan.0 in n 1536750519.339 * [misc]backup-simplify: Simplify +nan.0 into +nan.0 1536750519.339 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 1536750519.339 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.339 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 1536750519.339 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 1536750519.339 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.339 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.339 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.339 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.339 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.339 * [misc]taylor: Taking taylor expansion of k in n 1536750519.340 * [misc]backup-simplify: Simplify k into k 1536750519.340 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.340 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.340 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.340 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n 1536750519.340 * [misc]taylor: Taking taylor expansion of (/ -1 n) in n 1536750519.340 * [misc]taylor: Taking taylor expansion of -1 in n 1536750519.340 * [misc]backup-simplify: Simplify -1 into -1 1536750519.340 * [misc]taylor: Taking taylor expansion of n in n 1536750519.340 * [misc]backup-simplify: Simplify 0 into 0 1536750519.340 * [misc]backup-simplify: Simplify 1 into 1 1536750519.340 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750519.340 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536750519.340 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.340 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.341 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536750519.341 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 1536750519.341 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536750519.342 * [misc]taylor: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536750519.342 * [misc]taylor: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536750519.342 * [misc]taylor: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.342 * [misc]taylor: Taking taylor expansion of (log 2) in n 1536750519.342 * [misc]taylor: Taking taylor expansion of 2 in n 1536750519.342 * [misc]backup-simplify: Simplify 2 into 2 1536750519.342 * [misc]backup-simplify: Simplify (log 2) into (log 2) 1536750519.342 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.342 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.342 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.342 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.342 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.342 * [misc]taylor: Taking taylor expansion of k in n 1536750519.342 * [misc]backup-simplify: Simplify k into k 1536750519.342 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.342 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.342 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.342 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.342 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.343 * [misc]backup-simplify: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.343 * [misc]backup-simplify: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.343 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.343 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1536750519.343 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1536750519.343 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.343 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.343 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.343 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.343 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.343 * [misc]taylor: Taking taylor expansion of k in n 1536750519.343 * [misc]backup-simplify: Simplify k into k 1536750519.343 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.343 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.344 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.344 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.344 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.344 * [misc]backup-simplify: Simplify PI into PI 1536750519.344 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.344 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.344 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.345 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1536750519.345 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.345 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.346 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750519.347 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536750519.349 * [misc]backup-simplify: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.350 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750519.351 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536750519.352 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536750519.354 * [misc]backup-simplify: Simplify (+ (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536750519.355 * [misc]backup-simplify: Simplify (- (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536750519.356 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 1536750519.361 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))))) into (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k))))))) 1536750519.361 * * * * [misc]progress: [ 3 / 4 ] generating series at (2 2) 1536750519.362 * [misc]backup-simplify: Simplify (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) into (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 1536750519.362 * [misc]approximate: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in (n k) around 0 1536750519.362 * [misc]taylor: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1536750519.362 * [misc]taylor: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 1536750519.362 * [misc]taylor: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 1536750519.362 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 1536750519.362 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 1536750519.362 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750519.362 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.362 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.362 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750519.362 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.362 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.362 * [misc]taylor: Taking taylor expansion of k in k 1536750519.362 * [misc]backup-simplify: Simplify 0 into 0 1536750519.362 * [misc]backup-simplify: Simplify 1 into 1 1536750519.362 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750519.362 * [misc]taylor: Taking taylor expansion of n in k 1536750519.362 * [misc]backup-simplify: Simplify n into n 1536750519.362 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750519.362 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750519.363 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.363 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.363 * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 1536750519.363 * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 1536750519.363 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536750519.363 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536750519.363 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536750519.363 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750519.363 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.363 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.363 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750519.363 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.363 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.363 * [misc]taylor: Taking taylor expansion of k in k 1536750519.363 * [misc]backup-simplify: Simplify 0 into 0 1536750519.363 * [misc]backup-simplify: Simplify 1 into 1 1536750519.363 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.363 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.363 * [misc]backup-simplify: Simplify PI into PI 1536750519.364 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.364 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750519.364 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.364 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.365 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750519.365 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536750519.366 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536750519.366 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.366 * [misc]taylor: Taking taylor expansion of k in k 1536750519.366 * [misc]backup-simplify: Simplify 0 into 0 1536750519.366 * [misc]backup-simplify: Simplify 1 into 1 1536750519.366 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.366 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.367 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750519.367 * [misc]taylor: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 1536750519.367 * [misc]taylor: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 1536750519.367 * [misc]taylor: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 1536750519.367 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 1536750519.367 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 1536750519.367 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750519.367 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.367 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.367 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750519.367 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.367 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.367 * [misc]taylor: Taking taylor expansion of k in n 1536750519.367 * [misc]backup-simplify: Simplify k into k 1536750519.367 * [misc]taylor: Taking taylor expansion of (log n) in n 1536750519.367 * [misc]taylor: Taking taylor expansion of n in n 1536750519.367 * [misc]backup-simplify: Simplify 0 into 0 1536750519.367 * [misc]backup-simplify: Simplify 1 into 1 1536750519.368 * [misc]backup-simplify: Simplify (log 1) into 0 1536750519.368 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750519.368 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750519.368 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750519.368 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536750519.368 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 1536750519.368 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 1536750519.368 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 1536750519.368 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 1536750519.368 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 1536750519.369 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750519.369 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.369 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.369 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750519.369 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.369 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.369 * [misc]taylor: Taking taylor expansion of k in n 1536750519.369 * [misc]backup-simplify: Simplify k into k 1536750519.369 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.369 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.369 * [misc]backup-simplify: Simplify PI into PI 1536750519.369 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.369 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750519.369 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750519.369 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750519.370 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 1536750519.370 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 1536750519.370 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536750519.370 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.370 * [misc]taylor: Taking taylor expansion of k in n 1536750519.370 * [misc]backup-simplify: Simplify k into k 1536750519.370 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.370 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536750519.371 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750519.371 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536750519.371 * [misc]taylor: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 1536750519.371 * [misc]taylor: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 1536750519.371 * [misc]taylor: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 1536750519.371 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 1536750519.371 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 1536750519.371 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750519.371 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.371 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.371 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750519.371 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.371 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.371 * [misc]taylor: Taking taylor expansion of k in n 1536750519.371 * [misc]backup-simplify: Simplify k into k 1536750519.371 * [misc]taylor: Taking taylor expansion of (log n) in n 1536750519.371 * [misc]taylor: Taking taylor expansion of n in n 1536750519.371 * [misc]backup-simplify: Simplify 0 into 0 1536750519.371 * [misc]backup-simplify: Simplify 1 into 1 1536750519.371 * [misc]backup-simplify: Simplify (log 1) into 0 1536750519.371 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750519.372 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750519.372 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750519.372 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536750519.372 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 1536750519.372 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 1536750519.372 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 1536750519.372 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 1536750519.372 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 1536750519.372 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 1536750519.372 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.372 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.372 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in n 1536750519.372 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.372 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.372 * [misc]taylor: Taking taylor expansion of k in n 1536750519.372 * [misc]backup-simplify: Simplify k into k 1536750519.373 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.373 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.373 * [misc]backup-simplify: Simplify PI into PI 1536750519.373 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.373 * [misc]backup-simplify: Simplify (* 1/2 k) into (* 1/2 k) 1536750519.373 * [misc]backup-simplify: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 1536750519.373 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 1536750519.374 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 1536750519.374 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 1536750519.374 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in n 1536750519.374 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.374 * [misc]taylor: Taking taylor expansion of k in n 1536750519.374 * [misc]backup-simplify: Simplify k into k 1536750519.374 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.374 * [misc]backup-simplify: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1536750519.374 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750519.374 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1536750519.375 * [misc]backup-simplify: Simplify (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) into (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) 1536750519.375 * [misc]backup-simplify: Simplify (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) into (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 1536750519.375 * [misc]taylor: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 1536750519.375 * [misc]taylor: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 1536750519.375 * [misc]taylor: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 1536750519.375 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 1536750519.375 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 1536750519.375 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750519.375 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.375 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.376 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750519.376 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.376 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.376 * [misc]taylor: Taking taylor expansion of k in k 1536750519.376 * [misc]backup-simplify: Simplify 0 into 0 1536750519.376 * [misc]backup-simplify: Simplify 1 into 1 1536750519.376 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750519.376 * [misc]taylor: Taking taylor expansion of n in k 1536750519.376 * [misc]backup-simplify: Simplify n into n 1536750519.376 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750519.376 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750519.376 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.376 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.376 * [misc]backup-simplify: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 1536750519.377 * [misc]backup-simplify: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 1536750519.377 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536750519.377 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536750519.377 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536750519.377 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750519.377 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.377 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.377 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750519.377 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.377 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.377 * [misc]taylor: Taking taylor expansion of k in k 1536750519.377 * [misc]backup-simplify: Simplify 0 into 0 1536750519.377 * [misc]backup-simplify: Simplify 1 into 1 1536750519.377 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.377 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.377 * [misc]backup-simplify: Simplify PI into PI 1536750519.377 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.377 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750519.378 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.378 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.378 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750519.379 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536750519.379 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536750519.379 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.379 * [misc]taylor: Taking taylor expansion of k in k 1536750519.379 * [misc]backup-simplify: Simplify 0 into 0 1536750519.379 * [misc]backup-simplify: Simplify 1 into 1 1536750519.379 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.380 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.380 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750519.381 * [misc]backup-simplify: Simplify (* (pow n 1/2) (pow PI 1/2)) into (sqrt (* n PI)) 1536750519.381 * [misc]backup-simplify: Simplify (* (sqrt (* n PI)) 0) into 0 1536750519.381 * [misc]backup-simplify: Simplify 0 into 0 1536750519.383 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750519.384 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536750519.384 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.384 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.385 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log PI))) into 0 1536750519.386 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750519.388 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1536750519.388 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 k)) into 0 1536750519.388 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.389 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.389 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536750519.389 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log n))) into 0 1536750519.389 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750519.390 * [misc]backup-simplify: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (* 0 (pow PI (- 1/2 (* 1/2 k))))) into 0 1536750519.390 * [misc]backup-simplify: Simplify (+ (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) 0) (* 0 (sqrt (/ 1 k)))) into 0 1536750519.390 * [misc]taylor: Taking taylor expansion of 0 in k 1536750519.390 * [misc]backup-simplify: Simplify 0 into 0 1536750519.392 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750519.392 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536750519.392 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750519.392 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750519.393 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 1536750519.395 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 1536750519.395 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1536750519.396 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536750519.396 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750519.396 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750519.396 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 1536750519.396 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 1536750519.397 * [misc]backup-simplify: Simplify (+ (* (pow n 1/2) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/2 (* (sqrt n) (log n))) (pow PI 1/2))) into (- (+ (* 1/2 (* (sqrt (* n PI)) (log PI))) (* 1/2 (* (sqrt (* n PI)) (log n))))) 1536750519.398 * [misc]backup-simplify: Simplify (+ (* (sqrt (* n PI)) +nan.0) (* (- (+ (* 1/2 (* (sqrt (* n PI)) (log PI))) (* 1/2 (* (sqrt (* n PI)) (log n))))) 0)) into (- (* +nan.0 (sqrt (* n PI)))) 1536750519.398 * [misc]backup-simplify: Simplify (- (* +nan.0 (sqrt (* n PI)))) into (- (* +nan.0 (sqrt (* n PI)))) 1536750519.398 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750519.399 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 1536750519.402 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536750519.402 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536750519.402 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.402 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.403 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 1536750519.404 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750519.407 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 1536750519.407 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 1536750519.407 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.407 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.407 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536750519.408 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 1536750519.409 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750519.409 * [misc]backup-simplify: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 k)))))) into 0 1536750519.409 * [misc]backup-simplify: Simplify (+ (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 1536750519.409 * [misc]taylor: Taking taylor expansion of 0 in k 1536750519.409 * [misc]backup-simplify: Simplify 0 into 0 1536750519.409 * [misc]backup-simplify: Simplify 0 into 0 1536750519.410 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536750519.410 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750519.413 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536750519.413 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536750519.414 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.414 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.414 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 1536750519.418 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1536750519.419 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1536750519.419 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536750519.419 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.419 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.420 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 1536750519.421 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 1536750519.424 * [misc]backup-simplify: Simplify (+ (* (pow n 1/2) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow PI 1/2)))) into (+ (* 1/8 (* (sqrt (* n PI)) (pow (log n) 2))) (+ (* 1/4 (* (sqrt (* n PI)) (* (log PI) (log n)))) (* 1/8 (* (sqrt (* n PI)) (pow (log PI) 2))))) 1536750519.428 * [misc]backup-simplify: Simplify (+ (* (sqrt (* n PI)) +nan.0) (+ (* (- (+ (* 1/2 (* (sqrt (* n PI)) (log PI))) (* 1/2 (* (sqrt (* n PI)) (log n))))) +nan.0) (* (+ (* 1/8 (* (sqrt (* n PI)) (pow (log n) 2))) (+ (* 1/4 (* (sqrt (* n PI)) (* (log PI) (log n)))) (* 1/8 (* (sqrt (* n PI)) (pow (log PI) 2))))) 0))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (* +nan.0 (sqrt (* n PI)))))))) 1536750519.429 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (* +nan.0 (sqrt (* n PI)))))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (* +nan.0 (sqrt (* n PI)))))))) 1536750519.429 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750519.429 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 1536750519.434 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536750519.434 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1536750519.434 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.434 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.435 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1536750519.437 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log PI))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750519.441 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 1536750519.442 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 1536750519.442 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.442 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.442 * [misc]backup-simplify: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1536750519.442 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 1536750519.445 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750519.445 * [misc]backup-simplify: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 k))))))) into 0 1536750519.445 * [misc]backup-simplify: Simplify (+ (* (* (pow n (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 1536750519.445 * [misc]taylor: Taking taylor expansion of 0 in k 1536750519.446 * [misc]backup-simplify: Simplify 0 into 0 1536750519.446 * [misc]backup-simplify: Simplify 0 into 0 1536750519.446 * [misc]backup-simplify: Simplify 0 into 0 1536750519.446 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750519.446 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750519.451 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536750519.451 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536750519.452 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.452 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.453 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1536750519.459 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) 1536750519.461 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 1536750519.461 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536750519.461 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.461 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.462 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log n))))) into 0 1536750519.463 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 3) 6)) (* (/ (pow (- (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt n) (pow (log n) 3))) 1536750519.473 * [misc]backup-simplify: Simplify (+ (* (pow n 1/2) (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt n) (log n))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) (pow PI 1/2))))) into (- (+ (* 1/48 (* (sqrt (* n PI)) (pow (log PI) 3))) (+ (* 1/16 (* (sqrt (* n PI)) (* (pow (log PI) 2) (log n)))) (+ (* 1/48 (* (sqrt (* n PI)) (pow (log n) 3))) (* 1/16 (* (sqrt (* n PI)) (* (log PI) (pow (log n) 2)))))))) 1536750519.494 * [misc]backup-simplify: Simplify (+ (* (sqrt (* n PI)) +nan.0) (+ (* (- (+ (* 1/2 (* (sqrt (* n PI)) (log PI))) (* 1/2 (* (sqrt (* n PI)) (log n))))) +nan.0) (+ (* (+ (* 1/8 (* (sqrt (* n PI)) (pow (log n) 2))) (+ (* 1/4 (* (sqrt (* n PI)) (* (log PI) (log n)))) (* 1/8 (* (sqrt (* n PI)) (pow (log PI) 2))))) +nan.0) (* (- (+ (* 1/48 (* (sqrt (* n PI)) (pow (log PI) 3))) (+ (* 1/16 (* (sqrt (* n PI)) (* (pow (log PI) 2) (log n)))) (+ (* 1/48 (* (sqrt (* n PI)) (pow (log n) 3))) (* 1/16 (* (sqrt (* n PI)) (* (log PI) (pow (log n) 2)))))))) 0)))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log n) 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (log n)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log PI) 2))) (- (* +nan.0 (sqrt (* n PI)))))))))))))) 1536750519.506 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log n) 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (log n)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log PI) 2))) (- (* +nan.0 (sqrt (* n PI)))))))))))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log n) 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (log n)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log PI) 2))) (- (* +nan.0 (sqrt (* n PI)))))))))))))) 1536750519.524 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log n) 2))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (log n)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (pow (log PI) 2))) (- (* +nan.0 (sqrt (* n PI)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt (* n PI)) (log PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (log n))) (- (* +nan.0 (sqrt (* n PI)))))))) (* k 1)) (- (* +nan.0 (sqrt (* n PI)))))) into (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (pow k 2)))) (- (+ (* +nan.0 (sqrt (* n PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) k))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) k))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log n) 2) (pow k 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (pow k 2)))))))))))))))))))))) 1536750519.524 * [misc]backup-simplify: Simplify (* (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) into (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 1536750519.525 * [misc]approximate: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in (n k) around 0 1536750519.525 * [misc]taylor: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1536750519.525 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 1536750519.525 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750519.525 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536750519.525 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536750519.525 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750519.525 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.525 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.525 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.525 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.525 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.525 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.525 * [misc]taylor: Taking taylor expansion of k in k 1536750519.525 * [misc]backup-simplify: Simplify 0 into 0 1536750519.525 * [misc]backup-simplify: Simplify 1 into 1 1536750519.525 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.525 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.525 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.526 * [misc]backup-simplify: Simplify PI into PI 1536750519.526 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.526 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.526 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750519.526 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750519.527 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536750519.527 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.527 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750519.527 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 1536750519.527 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 1536750519.527 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750519.527 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.527 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.527 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.528 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.528 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.528 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.528 * [misc]taylor: Taking taylor expansion of k in k 1536750519.528 * [misc]backup-simplify: Simplify 0 into 0 1536750519.528 * [misc]backup-simplify: Simplify 1 into 1 1536750519.528 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.528 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in k 1536750519.528 * [misc]taylor: Taking taylor expansion of (/ 1 n) in k 1536750519.528 * [misc]taylor: Taking taylor expansion of n in k 1536750519.528 * [misc]backup-simplify: Simplify n into n 1536750519.528 * [misc]backup-simplify: Simplify (/ 1 n) into (/ 1 n) 1536750519.528 * [misc]backup-simplify: Simplify (log (/ 1 n)) into (log (/ 1 n)) 1536750519.528 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.528 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750519.528 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750519.528 * [misc]backup-simplify: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 1536750519.528 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.528 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536750519.528 * [misc]taylor: Taking taylor expansion of k in k 1536750519.528 * [misc]backup-simplify: Simplify 0 into 0 1536750519.528 * [misc]backup-simplify: Simplify 1 into 1 1536750519.529 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.529 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750519.529 * [misc]taylor: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 1536750519.529 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750519.529 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.529 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1536750519.529 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1536750519.529 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.529 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.529 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.529 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.529 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.529 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.529 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.529 * [misc]taylor: Taking taylor expansion of k in n 1536750519.529 * [misc]backup-simplify: Simplify k into k 1536750519.529 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.529 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.529 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.529 * [misc]backup-simplify: Simplify PI into PI 1536750519.529 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.529 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.529 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.530 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.530 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1536750519.530 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.530 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.530 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 1536750519.530 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 1536750519.530 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.530 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.530 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.530 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.530 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.530 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.530 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.530 * [misc]taylor: Taking taylor expansion of k in n 1536750519.530 * [misc]backup-simplify: Simplify k into k 1536750519.530 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.530 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in n 1536750519.530 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n 1536750519.530 * [misc]taylor: Taking taylor expansion of n in n 1536750519.530 * [misc]backup-simplify: Simplify 0 into 0 1536750519.530 * [misc]backup-simplify: Simplify 1 into 1 1536750519.531 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.531 * [misc]backup-simplify: Simplify (log 1) into 0 1536750519.531 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.531 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.531 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.531 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536750519.531 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 1536750519.531 * [misc]backup-simplify: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 1536750519.531 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536750519.531 * [misc]taylor: Taking taylor expansion of k in n 1536750519.531 * [misc]backup-simplify: Simplify k into k 1536750519.531 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536750519.531 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536750519.531 * [misc]taylor: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 1536750519.531 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 1536750519.531 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.531 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 1536750519.531 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 1536750519.531 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.531 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.532 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.532 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.532 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.532 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.532 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.532 * [misc]taylor: Taking taylor expansion of k in n 1536750519.532 * [misc]backup-simplify: Simplify k into k 1536750519.532 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.532 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.532 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.532 * [misc]backup-simplify: Simplify PI into PI 1536750519.532 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.532 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.532 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.532 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.532 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 1536750519.533 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.533 * [misc]taylor: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 1536750519.533 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 1536750519.533 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 1536750519.533 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 1536750519.533 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.533 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.533 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.533 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.533 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.533 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.533 * [misc]taylor: Taking taylor expansion of k in n 1536750519.533 * [misc]backup-simplify: Simplify k into k 1536750519.533 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.533 * [misc]taylor: Taking taylor expansion of (log (/ 1 n)) in n 1536750519.533 * [misc]taylor: Taking taylor expansion of (/ 1 n) in n 1536750519.533 * [misc]taylor: Taking taylor expansion of n in n 1536750519.533 * [misc]backup-simplify: Simplify 0 into 0 1536750519.533 * [misc]backup-simplify: Simplify 1 into 1 1536750519.533 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.533 * [misc]backup-simplify: Simplify (log 1) into 0 1536750519.533 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.533 * [misc]backup-simplify: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 1536750519.533 * [misc]backup-simplify: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 1536750519.533 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536750519.534 * [misc]backup-simplify: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 1536750519.534 * [misc]backup-simplify: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 1536750519.534 * [misc]taylor: Taking taylor expansion of (sqrt k) in n 1536750519.534 * [misc]taylor: Taking taylor expansion of k in n 1536750519.534 * [misc]backup-simplify: Simplify k into k 1536750519.534 * [misc]backup-simplify: Simplify (sqrt k) into (sqrt k) 1536750519.534 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt k))) into 0 1536750519.534 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 1536750519.534 * [misc]backup-simplify: Simplify (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) into (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 1536750519.534 * [misc]taylor: Taking taylor expansion of (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 1536750519.534 * [misc]taylor: Taking taylor expansion of (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) in k 1536750519.534 * [misc]taylor: Taking taylor expansion of (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k 1536750519.534 * [misc]taylor: Taking taylor expansion of (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k 1536750519.534 * [misc]taylor: Taking taylor expansion of -1 in k 1536750519.534 * [misc]backup-simplify: Simplify -1 into -1 1536750519.534 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k 1536750519.534 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750519.535 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.535 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.535 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.535 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.535 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.535 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.535 * [misc]taylor: Taking taylor expansion of k in k 1536750519.535 * [misc]backup-simplify: Simplify 0 into 0 1536750519.535 * [misc]backup-simplify: Simplify 1 into 1 1536750519.535 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.535 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750519.535 * [misc]taylor: Taking taylor expansion of n in k 1536750519.535 * [misc]backup-simplify: Simplify n into n 1536750519.535 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750519.535 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.535 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750519.535 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750519.535 * [misc]backup-simplify: Simplify (* -1/2 (log n)) into (* -1/2 (log n)) 1536750519.535 * [misc]backup-simplify: Simplify (* -1 (* -1/2 (log n))) into (* 1/2 (log n)) 1536750519.535 * [misc]backup-simplify: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 1536750519.535 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750519.535 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536750519.535 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536750519.535 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750519.535 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.535 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.536 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.536 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.536 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.536 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.536 * [misc]taylor: Taking taylor expansion of k in k 1536750519.536 * [misc]backup-simplify: Simplify 0 into 0 1536750519.536 * [misc]backup-simplify: Simplify 1 into 1 1536750519.536 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.536 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.536 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.536 * [misc]backup-simplify: Simplify PI into PI 1536750519.536 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.536 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.536 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750519.536 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750519.537 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536750519.537 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.537 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536750519.537 * [misc]taylor: Taking taylor expansion of k in k 1536750519.537 * [misc]backup-simplify: Simplify 0 into 0 1536750519.537 * [misc]backup-simplify: Simplify 1 into 1 1536750519.537 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.537 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750519.538 * [misc]backup-simplify: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 1536750519.538 * [misc]backup-simplify: Simplify (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 1536750519.538 * [misc]backup-simplify: Simplify 0 into 0 1536750519.538 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536750519.539 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 1536750519.540 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750519.540 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750519.540 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.540 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.540 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536750519.540 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 1536750519.541 * [misc]backup-simplify: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750519.543 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750519.543 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750519.543 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750519.543 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.543 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.543 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0 1536750519.544 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750519.544 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) into 0 1536750519.545 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (sqrt k))) into 0 1536750519.545 * [misc]taylor: Taking taylor expansion of 0 in k 1536750519.545 * [misc]backup-simplify: Simplify 0 into 0 1536750519.545 * [misc]backup-simplify: Simplify 0 into 0 1536750519.545 * [misc]backup-simplify: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (* 0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into 0 1536750519.545 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536750519.546 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536750519.546 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 1536750519.546 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750519.549 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 1536750519.549 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750519.550 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750519.550 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.550 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.550 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536750519.550 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 1536750519.551 * [misc]backup-simplify: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750519.555 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536750519.555 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750519.555 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750519.555 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.555 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.556 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 1536750519.557 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750519.557 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))))) into 0 1536750519.558 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 1536750519.558 * [misc]taylor: Taking taylor expansion of 0 in k 1536750519.558 * [misc]backup-simplify: Simplify 0 into 0 1536750519.558 * [misc]backup-simplify: Simplify 0 into 0 1536750519.558 * [misc]backup-simplify: Simplify 0 into 0 1536750519.559 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750519.559 * [misc]backup-simplify: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into 0 1536750519.559 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536750519.560 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536750519.560 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 1536750519.561 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750519.569 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 1536750519.569 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750519.569 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536750519.569 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.570 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.570 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 1536750519.570 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 1536750519.574 * [misc]backup-simplify: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750519.585 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536750519.585 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750519.585 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 1536750519.586 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.586 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.587 * [misc]backup-simplify: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1536750519.591 * [misc]backup-simplify: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1536750519.592 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))))) into 0 1536750519.592 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 1536750519.592 * [misc]taylor: Taking taylor expansion of 0 in k 1536750519.592 * [misc]backup-simplify: Simplify 0 into 0 1536750519.592 * [misc]backup-simplify: Simplify 0 into 0 1536750519.592 * [misc]backup-simplify: Simplify 0 into 0 1536750519.593 * [misc]backup-simplify: Simplify 0 into 0 1536750519.594 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750519.595 * [misc]backup-simplify: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 1536750519.595 * [misc]backup-simplify: Simplify (+ (* (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536750519.596 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 1536750519.599 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1536750519.599 * [misc]backup-simplify: Simplify (* (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) into (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 1536750519.599 * [misc]approximate: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in (n k) around 0 1536750519.599 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 1536750519.599 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 1536750519.599 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750519.599 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 1536750519.599 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 1536750519.600 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750519.600 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.600 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.600 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.600 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.600 * [misc]taylor: Taking taylor expansion of k in k 1536750519.600 * [misc]backup-simplify: Simplify 0 into 0 1536750519.600 * [misc]backup-simplify: Simplify 1 into 1 1536750519.600 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.600 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.600 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.600 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in k 1536750519.600 * [misc]taylor: Taking taylor expansion of (/ -1 n) in k 1536750519.600 * [misc]taylor: Taking taylor expansion of -1 in k 1536750519.600 * [misc]backup-simplify: Simplify -1 into -1 1536750519.600 * [misc]taylor: Taking taylor expansion of n in k 1536750519.600 * [misc]backup-simplify: Simplify n into n 1536750519.600 * [misc]backup-simplify: Simplify (/ -1 n) into (/ -1 n) 1536750519.600 * [misc]backup-simplify: Simplify (log (/ -1 n)) into (log (/ -1 n)) 1536750519.601 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.601 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.601 * [misc]backup-simplify: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 1536750519.601 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.601 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750519.601 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536750519.601 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536750519.601 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750519.601 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.601 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.601 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.601 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.601 * [misc]taylor: Taking taylor expansion of k in k 1536750519.601 * [misc]backup-simplify: Simplify 0 into 0 1536750519.601 * [misc]backup-simplify: Simplify 1 into 1 1536750519.601 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.602 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.602 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.602 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.602 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.602 * [misc]backup-simplify: Simplify PI into PI 1536750519.602 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.602 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.602 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.603 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750519.603 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.603 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536750519.603 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536750519.604 * [misc]taylor: Taking taylor expansion of -1 in k 1536750519.604 * [misc]backup-simplify: Simplify -1 into -1 1536750519.604 * [misc]taylor: Taking taylor expansion of k in k 1536750519.604 * [misc]backup-simplify: Simplify 0 into 0 1536750519.604 * [misc]backup-simplify: Simplify 1 into 1 1536750519.604 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750519.604 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.604 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536750519.605 * [misc]backup-simplify: Simplify (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.605 * [misc]backup-simplify: Simplify (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750519.605 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 1536750519.605 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536750519.605 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.605 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 1536750519.605 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 1536750519.605 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.605 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.605 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.605 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.605 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.606 * [misc]taylor: Taking taylor expansion of k in n 1536750519.606 * [misc]backup-simplify: Simplify k into k 1536750519.606 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.606 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.606 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.606 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n 1536750519.606 * [misc]taylor: Taking taylor expansion of (/ -1 n) in n 1536750519.606 * [misc]taylor: Taking taylor expansion of -1 in n 1536750519.606 * [misc]backup-simplify: Simplify -1 into -1 1536750519.606 * [misc]taylor: Taking taylor expansion of n in n 1536750519.606 * [misc]backup-simplify: Simplify 0 into 0 1536750519.606 * [misc]backup-simplify: Simplify 1 into 1 1536750519.606 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750519.606 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536750519.606 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.606 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.607 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536750519.607 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 1536750519.607 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536750519.607 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.608 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1536750519.608 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1536750519.608 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.608 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.608 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.608 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.608 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.608 * [misc]taylor: Taking taylor expansion of k in n 1536750519.608 * [misc]backup-simplify: Simplify k into k 1536750519.608 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.608 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.608 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.608 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.608 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.608 * [misc]backup-simplify: Simplify PI into PI 1536750519.608 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.608 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.608 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.609 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1536750519.609 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.609 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536750519.609 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536750519.609 * [misc]taylor: Taking taylor expansion of -1 in n 1536750519.609 * [misc]backup-simplify: Simplify -1 into -1 1536750519.609 * [misc]taylor: Taking taylor expansion of k in n 1536750519.609 * [misc]backup-simplify: Simplify k into k 1536750519.610 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536750519.610 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536750519.610 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536750519.610 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536750519.610 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.611 * [misc]backup-simplify: Simplify (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) into (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 1536750519.611 * [misc]taylor: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 1536750519.611 * [misc]taylor: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 1536750519.611 * [misc]taylor: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.611 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 1536750519.611 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 1536750519.611 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.611 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.611 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.611 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.611 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.611 * [misc]taylor: Taking taylor expansion of k in n 1536750519.611 * [misc]backup-simplify: Simplify k into k 1536750519.612 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.612 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.612 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.612 * [misc]taylor: Taking taylor expansion of (log (/ -1 n)) in n 1536750519.612 * [misc]taylor: Taking taylor expansion of (/ -1 n) in n 1536750519.612 * [misc]taylor: Taking taylor expansion of -1 in n 1536750519.612 * [misc]backup-simplify: Simplify -1 into -1 1536750519.612 * [misc]taylor: Taking taylor expansion of n in n 1536750519.612 * [misc]backup-simplify: Simplify 0 into 0 1536750519.612 * [misc]backup-simplify: Simplify 1 into 1 1536750519.612 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750519.612 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536750519.612 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.612 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.613 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536750519.613 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 1536750519.614 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536750519.614 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 1536750519.614 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 1536750519.614 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 1536750519.614 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 1536750519.614 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 1536750519.614 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.614 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.614 * [misc]taylor: Taking taylor expansion of (/ 1 k) in n 1536750519.614 * [misc]taylor: Taking taylor expansion of k in n 1536750519.614 * [misc]backup-simplify: Simplify k into k 1536750519.614 * [misc]backup-simplify: Simplify (/ 1 k) into (/ 1 k) 1536750519.614 * [misc]taylor: Taking taylor expansion of 1/2 in n 1536750519.614 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.614 * [misc]taylor: Taking taylor expansion of (log PI) in n 1536750519.614 * [misc]taylor: Taking taylor expansion of PI in n 1536750519.614 * [misc]backup-simplify: Simplify PI into PI 1536750519.614 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.614 * [misc]backup-simplify: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 1536750519.615 * [misc]backup-simplify: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 1536750519.615 * [misc]backup-simplify: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 1536750519.616 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.616 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in n 1536750519.616 * [misc]taylor: Taking taylor expansion of (/ -1 k) in n 1536750519.616 * [misc]taylor: Taking taylor expansion of -1 in n 1536750519.616 * [misc]backup-simplify: Simplify -1 into -1 1536750519.616 * [misc]taylor: Taking taylor expansion of k in n 1536750519.616 * [misc]backup-simplify: Simplify k into k 1536750519.616 * [misc]backup-simplify: Simplify (/ -1 k) into (/ -1 k) 1536750519.616 * [misc]backup-simplify: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1536750519.616 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1536750519.616 * [misc]backup-simplify: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1536750519.617 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.617 * [misc]backup-simplify: Simplify (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) into (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 1536750519.617 * [misc]taylor: Taking taylor expansion of (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 1536750519.617 * [misc]taylor: Taking taylor expansion of (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 1536750519.618 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k 1536750519.618 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k 1536750519.618 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750519.618 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.618 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.618 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.618 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.618 * [misc]taylor: Taking taylor expansion of k in k 1536750519.618 * [misc]backup-simplify: Simplify 0 into 0 1536750519.618 * [misc]backup-simplify: Simplify 1 into 1 1536750519.618 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.618 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.618 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.618 * [misc]taylor: Taking taylor expansion of (- (log -1) (log n)) in k 1536750519.618 * [misc]taylor: Taking taylor expansion of (log -1) in k 1536750519.618 * [misc]taylor: Taking taylor expansion of -1 in k 1536750519.619 * [misc]backup-simplify: Simplify -1 into -1 1536750519.619 * [misc]backup-simplify: Simplify (log -1) into (log -1) 1536750519.619 * [misc]taylor: Taking taylor expansion of (log n) in k 1536750519.619 * [misc]taylor: Taking taylor expansion of n in k 1536750519.619 * [misc]backup-simplify: Simplify n into n 1536750519.619 * [misc]backup-simplify: Simplify (log n) into (log n) 1536750519.619 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.619 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.619 * [misc]backup-simplify: Simplify (- (log n)) into (- (log n)) 1536750519.619 * [misc]backup-simplify: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 1536750519.620 * [misc]backup-simplify: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) 1536750519.620 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 1536750519.620 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750519.620 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536750519.620 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536750519.620 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750519.620 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.620 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.620 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.620 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.620 * [misc]taylor: Taking taylor expansion of k in k 1536750519.620 * [misc]backup-simplify: Simplify 0 into 0 1536750519.620 * [misc]backup-simplify: Simplify 1 into 1 1536750519.620 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.620 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.620 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.621 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.621 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.621 * [misc]backup-simplify: Simplify PI into PI 1536750519.621 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.621 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.621 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.622 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750519.622 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.622 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536750519.622 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536750519.622 * [misc]taylor: Taking taylor expansion of -1 in k 1536750519.622 * [misc]backup-simplify: Simplify -1 into -1 1536750519.623 * [misc]taylor: Taking taylor expansion of k in k 1536750519.623 * [misc]backup-simplify: Simplify 0 into 0 1536750519.623 * [misc]backup-simplify: Simplify 1 into 1 1536750519.623 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750519.623 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.623 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536750519.624 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.624 * [misc]backup-simplify: Simplify (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750519.625 * [misc]backup-simplify: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750519.628 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750519.628 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750519.628 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750519.629 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.629 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 1536750519.631 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750519.631 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536750519.633 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 1536750519.634 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1536750519.634 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 1536750519.634 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.634 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536750519.635 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 1536750519.636 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 1536750519.637 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 1536750519.638 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 1536750519.638 * [misc]taylor: Taking taylor expansion of 0 in k 1536750519.638 * [misc]backup-simplify: Simplify 0 into 0 1536750519.638 * [misc]backup-simplify: Simplify 0 into 0 1536750519.638 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 1536750519.639 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536750519.640 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750519.641 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536750519.641 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536750519.646 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536750519.647 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750519.647 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750519.647 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.648 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (log PI)))) into 0 1536750519.650 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750519.651 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750519.655 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 1536750519.655 * [misc]backup-simplify: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750519.656 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 1536750519.656 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.656 * [misc]backup-simplify: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 1536750519.657 * [misc]backup-simplify: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 1536750519.659 * [misc]backup-simplify: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1536750519.660 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1536750519.660 * [misc]backup-simplify: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1536750519.660 * [misc]backup-simplify: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 1536750519.661 * [misc]backup-simplify: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 1536750519.661 * [misc]taylor: Taking taylor expansion of 0 in k 1536750519.661 * [misc]backup-simplify: Simplify 0 into 0 1536750519.661 * [misc]backup-simplify: Simplify 0 into 0 1536750519.661 * [misc]backup-simplify: Simplify 0 into 0 1536750519.661 * [misc]backup-simplify: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 1536750519.661 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750519.662 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750519.663 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536750519.664 * [misc]backup-simplify: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 1536750519.665 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) into (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))))))))) 1536750519.665 * * * * [misc]progress: [ 4 / 4 ] generating series at (2 2 2) 1536750519.666 * [misc]backup-simplify: Simplify (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k)))) 1536750519.666 * [misc]approximate: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k)))) in (k) around 0 1536750519.666 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k)))) in k 1536750519.666 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536750519.666 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.666 * [misc]taylor: Taking taylor expansion of k in k 1536750519.666 * [misc]backup-simplify: Simplify 0 into 0 1536750519.666 * [misc]backup-simplify: Simplify 1 into 1 1536750519.666 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.666 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.666 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750519.666 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536750519.666 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536750519.667 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536750519.667 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750519.667 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.667 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.667 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750519.667 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.667 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.667 * [misc]taylor: Taking taylor expansion of k in k 1536750519.667 * [misc]backup-simplify: Simplify 0 into 0 1536750519.667 * [misc]backup-simplify: Simplify 1 into 1 1536750519.667 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.667 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.667 * [misc]backup-simplify: Simplify PI into PI 1536750519.667 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.667 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750519.667 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.667 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.668 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750519.668 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536750519.668 * [misc]taylor: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow PI (- 1/2 (* 1/2 k)))) in k 1536750519.668 * [misc]taylor: Taking taylor expansion of (sqrt (/ 1 k)) in k 1536750519.668 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.668 * [misc]taylor: Taking taylor expansion of k in k 1536750519.668 * [misc]backup-simplify: Simplify 0 into 0 1536750519.668 * [misc]backup-simplify: Simplify 1 into 1 1536750519.669 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.669 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.669 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750519.669 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 1536750519.669 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 1536750519.669 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 1536750519.669 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 1536750519.669 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.669 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.669 * [misc]taylor: Taking taylor expansion of (* 1/2 k) in k 1536750519.669 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.669 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.669 * [misc]taylor: Taking taylor expansion of k in k 1536750519.669 * [misc]backup-simplify: Simplify 0 into 0 1536750519.669 * [misc]backup-simplify: Simplify 1 into 1 1536750519.669 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.669 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.669 * [misc]backup-simplify: Simplify PI into PI 1536750519.669 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.669 * [misc]backup-simplify: Simplify (* 1/2 0) into 0 1536750519.670 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.670 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.670 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750519.670 * [misc]backup-simplify: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 1536750519.671 * [misc]backup-simplify: Simplify (* 0 (pow PI 1/2)) into 0 1536750519.671 * [misc]backup-simplify: Simplify 0 into 0 1536750519.673 * [misc]backup-simplify: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 1536750519.673 * [misc]backup-simplify: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 1536750519.673 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750519.673 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750519.673 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 1536750519.676 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 1536750519.677 * [misc]backup-simplify: Simplify (+ (* 0 (* -1/2 (* (log PI) (sqrt PI)))) (* +nan.0 (pow PI 1/2))) into (- (* +nan.0 (sqrt PI))) 1536750519.678 * [misc]backup-simplify: Simplify (- (* +nan.0 (sqrt PI))) into (- (* +nan.0 (sqrt PI))) 1536750519.681 * [misc]backup-simplify: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 1536750519.681 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 1536750519.681 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.681 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.682 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 1536750519.685 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 1536750519.685 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1536750519.686 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750519.690 * [misc]backup-simplify: Simplify (+ (* 0 (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* +nan.0 (* -1/2 (* (log PI) (sqrt PI)))) (* +nan.0 (pow PI 1/2)))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) 1536750519.691 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) 1536750519.696 * [misc]backup-simplify: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 1536750519.696 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 1536750519.696 * [misc]backup-simplify: Simplify (- 0) into 0 1536750519.697 * [misc]backup-simplify: Simplify (+ 0 0) into 0 1536750519.698 * [misc]backup-simplify: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 1536750519.703 * [misc]backup-simplify: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) 1536750519.703 * [misc]backup-simplify: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750519.704 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750519.711 * [misc]backup-simplify: Simplify (+ (* 0 (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* +nan.0 (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* +nan.0 (* -1/2 (* (log PI) (sqrt PI)))) (* +nan.0 (pow PI 1/2))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) 1536750519.716 * [misc]backup-simplify: Simplify (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) into (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) 1536750519.725 * [misc]backup-simplify: Simplify (+ (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (pow (log PI) 2) (sqrt PI)))))))) (pow k 2)) (+ (* (- (+ (* +nan.0 (* (log PI) (sqrt PI))) (- (* +nan.0 (sqrt PI))))) k) (- (* +nan.0 (sqrt PI))))) into (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (pow k 2))) (- (+ (* +nan.0 (* (* (log PI) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))))))))))))) 1536750519.725 * [misc]backup-simplify: Simplify (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 1536750519.725 * [misc]approximate: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (k) around 0 1536750519.725 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 1536750519.725 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750519.725 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536750519.725 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536750519.725 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750519.725 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.725 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.725 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.725 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.725 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.725 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.725 * [misc]taylor: Taking taylor expansion of k in k 1536750519.726 * [misc]backup-simplify: Simplify 0 into 0 1536750519.726 * [misc]backup-simplify: Simplify 1 into 1 1536750519.726 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.726 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.726 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.726 * [misc]backup-simplify: Simplify PI into PI 1536750519.726 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.726 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.726 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750519.726 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750519.727 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536750519.727 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.727 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536750519.727 * [misc]taylor: Taking taylor expansion of k in k 1536750519.727 * [misc]backup-simplify: Simplify 0 into 0 1536750519.727 * [misc]backup-simplify: Simplify 1 into 1 1536750519.727 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.727 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750519.727 * [misc]taylor: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 1536750519.727 * [misc]taylor: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 1536750519.727 * [misc]taylor: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 1536750519.728 * [misc]taylor: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 1536750519.728 * [misc]taylor: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 1536750519.728 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.728 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.728 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.728 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.728 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.728 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.728 * [misc]taylor: Taking taylor expansion of k in k 1536750519.728 * [misc]backup-simplify: Simplify 0 into 0 1536750519.728 * [misc]backup-simplify: Simplify 1 into 1 1536750519.728 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.728 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.728 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.728 * [misc]backup-simplify: Simplify PI into PI 1536750519.728 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.728 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.728 * [misc]backup-simplify: Simplify (- 1/2) into -1/2 1536750519.728 * [misc]backup-simplify: Simplify (+ 0 -1/2) into -1/2 1536750519.729 * [misc]backup-simplify: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 1536750519.729 * [misc]backup-simplify: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 1536750519.729 * [misc]taylor: Taking taylor expansion of (sqrt k) in k 1536750519.729 * [misc]taylor: Taking taylor expansion of k in k 1536750519.729 * [misc]backup-simplify: Simplify 0 into 0 1536750519.729 * [misc]backup-simplify: Simplify 1 into 1 1536750519.729 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.729 * [misc]backup-simplify: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1536750519.730 * [misc]backup-simplify: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) into 0 1536750519.730 * [misc]backup-simplify: Simplify 0 into 0 1536750519.730 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536750519.730 * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536750519.731 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750519.731 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536750519.731 * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536750519.732 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750519.732 * [misc]backup-simplify: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536750519.732 * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 1536750519.733 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))) (pow (/ 1 k) 3)) (+ (* (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))) (pow (/ 1 k) 2)) (* (- (* +nan.0 (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) k)) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 3))) (- (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 2)))))))) 1536750519.733 * [misc]backup-simplify: Simplify (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 1536750519.733 * [misc]approximate: Taking taylor expansion of (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k) around 0 1536750519.733 * [misc]taylor: Taking taylor expansion of (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1536750519.733 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750519.733 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536750519.733 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536750519.733 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750519.733 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.733 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.734 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.734 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.734 * [misc]taylor: Taking taylor expansion of k in k 1536750519.734 * [misc]backup-simplify: Simplify 0 into 0 1536750519.734 * [misc]backup-simplify: Simplify 1 into 1 1536750519.734 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.734 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.734 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.734 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.734 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.734 * [misc]backup-simplify: Simplify PI into PI 1536750519.734 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.734 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.734 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.735 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750519.735 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.735 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536750519.735 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536750519.735 * [misc]taylor: Taking taylor expansion of -1 in k 1536750519.735 * [misc]backup-simplify: Simplify -1 into -1 1536750519.735 * [misc]taylor: Taking taylor expansion of k in k 1536750519.735 * [misc]backup-simplify: Simplify 0 into 0 1536750519.735 * [misc]backup-simplify: Simplify 1 into 1 1536750519.735 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750519.735 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.736 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536750519.736 * [misc]backup-simplify: Simplify (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.736 * [misc]taylor: Taking taylor expansion of (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 1536750519.736 * [misc]taylor: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 1536750519.736 * [misc]taylor: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 1536750519.736 * [misc]taylor: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 1536750519.736 * [misc]taylor: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 1536750519.736 * [misc]taylor: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 1536750519.736 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.736 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.736 * [misc]taylor: Taking taylor expansion of (/ 1 k) in k 1536750519.736 * [misc]taylor: Taking taylor expansion of k in k 1536750519.736 * [misc]backup-simplify: Simplify 0 into 0 1536750519.736 * [misc]backup-simplify: Simplify 1 into 1 1536750519.736 * [misc]backup-simplify: Simplify (/ 1 1) into 1 1536750519.737 * [misc]taylor: Taking taylor expansion of 1/2 in k 1536750519.737 * [misc]backup-simplify: Simplify 1/2 into 1/2 1536750519.737 * [misc]taylor: Taking taylor expansion of (log PI) in k 1536750519.737 * [misc]taylor: Taking taylor expansion of PI in k 1536750519.737 * [misc]backup-simplify: Simplify PI into PI 1536750519.737 * [misc]backup-simplify: Simplify (log PI) into (log PI) 1536750519.737 * [misc]backup-simplify: Simplify (* 1/2 1) into 1/2 1536750519.737 * [misc]backup-simplify: Simplify (+ 1/2 0) into 1/2 1536750519.738 * [misc]backup-simplify: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 1536750519.738 * [misc]backup-simplify: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 1536750519.738 * [misc]taylor: Taking taylor expansion of (sqrt (/ -1 k)) in k 1536750519.738 * [misc]taylor: Taking taylor expansion of (/ -1 k) in k 1536750519.738 * [misc]taylor: Taking taylor expansion of -1 in k 1536750519.738 * [misc]backup-simplify: Simplify -1 into -1 1536750519.738 * [misc]taylor: Taking taylor expansion of k in k 1536750519.738 * [misc]backup-simplify: Simplify 0 into 0 1536750519.738 * [misc]backup-simplify: Simplify 1 into 1 1536750519.739 * [misc]backup-simplify: Simplify (/ -1 1) into -1 1536750519.739 * [misc]backup-simplify: Simplify (sqrt 0) into 0 1536750519.739 * [misc]backup-simplify: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1536750519.739 * [misc]backup-simplify: Simplify (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.740 * [misc]backup-simplify: Simplify (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 1536750519.740 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1536750519.741 * [misc]backup-simplify: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1536750519.742 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750519.742 * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750519.742 * [misc]backup-simplify: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1536750519.743 * [misc]backup-simplify: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1536750519.744 * [misc]backup-simplify: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750519.745 * [misc]backup-simplify: Simplify (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 1536750519.746 * [misc]backup-simplify: Simplify (+ (* (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))) (/ 1 (- k))) (* +nan.0 (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) into (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) k)) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 2))) (- (* +nan.0 (pow PI (- 1/2 (* 1/2 k))))))))) 1536750519.746 * * * [misc]progress: simplifying candidates 1536750519.746 * * * * [misc]progress: [ 1 / 144 ] simplifiying candidate # 1536750519.746 * * * * [misc]progress: [ 2 / 144 ] simplifiying candidate # 1536750519.747 * [enter]simplify: Simplifying (pow PI (/ k 2)) 1536750519.747 * * [misc]simplify: iters left: 3 (5 enodes) 1536750519.749 * [exit]simplify: Simplified to (pow PI (/ k 2)) 1536750519.749 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI 1/2) (pow PI (/ k 2))) (sqrt k))))) 1536750519.749 * * * * [misc]progress: [ 3 / 144 ] simplifiying candidate # 1536750519.749 * [enter]simplify: Simplifying (cbrt (- 1/2 (/ k 2))) 1536750519.750 * * [misc]simplify: iters left: 5 (6 enodes) 1536750519.752 * * [misc]simplify: iters left: 4 (8 enodes) 1536750519.755 * * [misc]simplify: iters left: 3 (11 enodes) 1536750519.758 * [exit]simplify: Simplified to (cbrt (- 1/2 (/ k 2))) 1536750519.758 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow (pow PI (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))))) 1536750519.758 * * * * [misc]progress: [ 4 / 144 ] simplifiying candidate # 1536750519.759 * [enter]simplify: Simplifying (sqrt (- 1/2 (/ k 2))) 1536750519.759 * * [misc]simplify: iters left: 5 (6 enodes) 1536750519.761 * * [misc]simplify: iters left: 4 (8 enodes) 1536750519.764 * * [misc]simplify: iters left: 3 (11 enodes) 1536750519.765 * [exit]simplify: Simplified to (sqrt (- 1/2 (/ k 2))) 1536750519.765 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow (pow PI (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))))) 1536750519.765 * * * * [misc]progress: [ 5 / 144 ] simplifiying candidate # 1536750519.766 * [enter]simplify: Simplifying (- 1/2 (/ k 2)) 1536750519.766 * * [misc]simplify: iters left: 4 (5 enodes) 1536750519.767 * * [misc]simplify: iters left: 3 (7 enodes) 1536750519.768 * * [misc]simplify: iters left: 2 (10 enodes) 1536750519.770 * [exit]simplify: Simplified to (- 1/2 (/ k 2)) 1536750519.770 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow (pow PI 1) (- 1/2 (/ k 2))) (sqrt k))))) 1536750519.770 * * * * [misc]progress: [ 6 / 144 ] simplifiying candidate # 1536750519.770 * [enter]simplify: Simplifying (pow PI (- (/ k 2))) 1536750519.770 * * [misc]simplify: iters left: 5 (6 enodes) 1536750519.771 * * [misc]simplify: iters left: 4 (8 enodes) 1536750519.773 * [exit]simplify: Simplified to (pow PI (/ (- k) 2)) 1536750519.773 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (* (pow PI 1/2) (pow PI (/ (- k) 2))) (sqrt k))))) 1536750519.773 * * * * [misc]progress: [ 7 / 144 ] simplifiying candidate # 1536750519.773 * [enter]simplify: Simplifying (pow PI (- (/ k 2))) 1536750519.773 * * [misc]simplify: iters left: 5 (6 enodes) 1536750519.774 * * [misc]simplify: iters left: 4 (8 enodes) 1536750519.776 * [exit]simplify: Simplified to (pow PI (/ (- k) 2)) 1536750519.776 * [misc]simplify: Simplified (2 2 2 1 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (* (pow PI 1/2) (pow PI (/ (- k) 2))) (sqrt k))))) 1536750519.776 * * * * [misc]progress: [ 8 / 144 ] simplifiying candidate # 1536750519.776 * * * * [misc]progress: [ 9 / 144 ] simplifiying candidate # 1536750519.776 * * * * [misc]progress: [ 10 / 144 ] simplifiying candidate # 1536750519.776 * * * * [misc]progress: [ 11 / 144 ] simplifiying candidate # 1536750519.776 * * * * [misc]progress: [ 12 / 144 ] simplifiying candidate # 1536750519.776 * * * * [misc]progress: [ 13 / 144 ] simplifiying candidate # 1536750519.776 * * * * [misc]progress: [ 14 / 144 ] simplifiying candidate # 1536750519.776 * * * * [misc]progress: [ 15 / 144 ] simplifiying candidate # 1536750519.776 * * * * [misc]progress: [ 16 / 144 ] simplifiying candidate # 1536750519.777 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (* (log n) (- 1/2 (/ k 2))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536750519.778 * * [misc]simplify: iters left: 6 (18 enodes) 1536750519.783 * * [misc]simplify: iters left: 5 (31 enodes) 1536750519.792 * * [misc]simplify: iters left: 4 (76 enodes) 1536750519.830 * * [misc]simplify: iters left: 3 (251 enodes) 1536750520.117 * [exit]simplify: Simplified to (- (* (+ (log 2) (+ (log n) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750520.118 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log 2) (+ (log n) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536750520.118 * * * * [misc]progress: [ 17 / 144 ] simplifiying candidate # 1536750520.118 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (* (log n) (- 1/2 (/ k 2))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k))))) 1536750520.119 * * [misc]simplify: iters left: 6 (18 enodes) 1536750520.124 * * [misc]simplify: iters left: 5 (32 enodes) 1536750520.134 * * [misc]simplify: iters left: 4 (72 enodes) 1536750520.165 * * [misc]simplify: iters left: 3 (217 enodes) 1536750520.487 * [exit]simplify: Simplified to (- (* (+ (log PI) (+ (log 2) (log n))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750520.487 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log PI) (+ (log 2) (log n))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536750520.487 * * * * [misc]progress: [ 18 / 144 ] simplifiying candidate # 1536750520.488 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (* (log n) (- 1/2 (/ k 2))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536750520.490 * * [misc]simplify: iters left: 6 (17 enodes) 1536750520.498 * * [misc]simplify: iters left: 5 (28 enodes) 1536750520.513 * * [misc]simplify: iters left: 4 (61 enodes) 1536750520.559 * * [misc]simplify: iters left: 3 (170 enodes) 1536750520.698 * [exit]simplify: Simplified to (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750520.698 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536750520.698 * * * * [misc]progress: [ 19 / 144 ] simplifiying candidate # 1536750520.698 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536750520.699 * * [misc]simplify: iters left: 6 (18 enodes) 1536750520.704 * * [misc]simplify: iters left: 5 (32 enodes) 1536750520.715 * * [misc]simplify: iters left: 4 (72 enodes) 1536750520.746 * * [misc]simplify: iters left: 3 (205 enodes) 1536750521.025 * [exit]simplify: Simplified to (- (* (+ (+ (log 2) (log PI)) (log n)) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750521.025 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (+ (log 2) (log PI)) (log n)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536750521.025 * * * * [misc]progress: [ 20 / 144 ] simplifiying candidate # 1536750521.025 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k))))) 1536750521.026 * * [misc]simplify: iters left: 6 (18 enodes) 1536750521.031 * * [misc]simplify: iters left: 5 (33 enodes) 1536750521.040 * * [misc]simplify: iters left: 4 (68 enodes) 1536750521.080 * * [misc]simplify: iters left: 3 (171 enodes) 1536750521.364 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (+ (log 2) (log PI)) (log n))) (log (sqrt k))) 1536750521.364 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (+ (log 2) (log PI)) (log n))) (log (sqrt k))))) 1536750521.365 * * * * [misc]progress: [ 21 / 144 ] simplifiying candidate # 1536750521.365 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (+ (log (pow n (- 1/2 (/ k 2)))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536750521.366 * * [misc]simplify: iters left: 6 (17 enodes) 1536750521.370 * * [misc]simplify: iters left: 5 (29 enodes) 1536750521.379 * * [misc]simplify: iters left: 4 (57 enodes) 1536750521.406 * * [misc]simplify: iters left: 3 (132 enodes) 1536750521.508 * * [misc]simplify: iters left: 2 (457 enodes) 1536750522.227 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (+ (log n) (log PI)) (log 2))) (log (sqrt k))) 1536750522.227 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (+ (log n) (log PI)) (log 2))) (log (sqrt k))))) 1536750522.227 * * * * [misc]progress: [ 22 / 144 ] simplifiying candidate # 1536750522.227 * [enter]simplify: Simplifying (+ (* (log 2) (- 1/2 (/ k 2))) (log (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536750522.229 * * [misc]simplify: iters left: 6 (16 enodes) 1536750522.237 * * [misc]simplify: iters left: 5 (26 enodes) 1536750522.245 * * [misc]simplify: iters left: 4 (51 enodes) 1536750522.258 * * [misc]simplify: iters left: 3 (101 enodes) 1536750522.306 * * [misc]simplify: iters left: 2 (236 enodes) 1536750522.665 * [exit]simplify: Simplified to (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750522.665 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536750522.665 * * * * [misc]progress: [ 23 / 144 ] simplifiying candidate # 1536750522.665 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (* (log n) (- 1/2 (/ k 2))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536750522.667 * * [misc]simplify: iters left: 6 (18 enodes) 1536750522.671 * * [misc]simplify: iters left: 5 (32 enodes) 1536750522.680 * * [misc]simplify: iters left: 4 (72 enodes) 1536750522.724 * * [misc]simplify: iters left: 3 (213 enodes) 1536750522.991 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (+ (log n) (log PI)))) (log (sqrt k))) 1536750522.991 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (+ (log n) (log PI)))) (log (sqrt k))))) 1536750522.991 * * * * [misc]progress: [ 24 / 144 ] simplifiying candidate # 1536750522.992 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (* (log n) (- 1/2 (/ k 2))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k))))) 1536750522.994 * * [misc]simplify: iters left: 6 (18 enodes) 1536750523.003 * * [misc]simplify: iters left: 5 (33 enodes) 1536750523.019 * * [misc]simplify: iters left: 4 (68 enodes) 1536750523.044 * * [misc]simplify: iters left: 3 (179 enodes) 1536750523.269 * [exit]simplify: Simplified to (- (* (+ (+ (log 2) (log PI)) (log n)) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750523.269 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (+ (log 2) (log PI)) (log n)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536750523.269 * * * * [misc]progress: [ 25 / 144 ] simplifiying candidate # 1536750523.269 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (* (log n) (- 1/2 (/ k 2))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536750523.271 * * [misc]simplify: iters left: 6 (17 enodes) 1536750523.279 * * [misc]simplify: iters left: 5 (29 enodes) 1536750523.294 * * [misc]simplify: iters left: 4 (57 enodes) 1536750523.313 * * [misc]simplify: iters left: 3 (140 enodes) 1536750523.413 * * [misc]simplify: iters left: 2 (467 enodes) 1536750524.164 * [exit]simplify: Simplified to (- (* (+ (log 2) (+ (log n) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750524.164 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log 2) (+ (log n) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536750524.164 * * * * [misc]progress: [ 26 / 144 ] simplifiying candidate # 1536750524.165 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536750524.167 * * [misc]simplify: iters left: 6 (18 enodes) 1536750524.176 * * [misc]simplify: iters left: 5 (33 enodes) 1536750524.193 * * [misc]simplify: iters left: 4 (68 enodes) 1536750524.236 * * [misc]simplify: iters left: 3 (167 enodes) 1536750524.522 * [exit]simplify: Simplified to (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750524.522 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536750524.522 * * * * [misc]progress: [ 27 / 144 ] simplifiying candidate # 1536750524.522 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (log (pow n (- 1/2 (/ k 2)))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k))))) 1536750524.525 * * [misc]simplify: iters left: 6 (18 enodes) 1536750524.534 * * [misc]simplify: iters left: 5 (34 enodes) 1536750524.550 * * [misc]simplify: iters left: 4 (64 enodes) 1536750524.573 * * [misc]simplify: iters left: 3 (133 enodes) 1536750524.831 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log 2) (+ (log PI) (log n)))) (log (sqrt k))) 1536750524.831 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (log 2) (+ (log PI) (log n)))) (log (sqrt k))))) 1536750524.831 * * * * [misc]progress: [ 28 / 144 ] simplifiying candidate # 1536750524.831 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (+ (log (pow n (- 1/2 (/ k 2)))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536750524.832 * * [misc]simplify: iters left: 6 (17 enodes) 1536750524.837 * * [misc]simplify: iters left: 5 (30 enodes) 1536750524.844 * * [misc]simplify: iters left: 4 (53 enodes) 1536750524.863 * * [misc]simplify: iters left: 3 (102 enodes) 1536750524.944 * * [misc]simplify: iters left: 2 (376 enodes) 1536750525.412 * [exit]simplify: Simplified to (- (* (+ (+ (log 2) (log PI)) (log n)) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750525.412 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (+ (+ (log 2) (log PI)) (log n)) (- 1/2 (/ k 2))) (log (sqrt k))))) 1536750525.412 * * * * [misc]progress: [ 29 / 144 ] simplifiying candidate # 1536750525.413 * [enter]simplify: Simplifying (+ (log (pow 2 (- 1/2 (/ k 2)))) (log (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536750525.414 * * [misc]simplify: iters left: 6 (16 enodes) 1536750525.418 * * [misc]simplify: iters left: 5 (27 enodes) 1536750525.424 * * [misc]simplify: iters left: 4 (47 enodes) 1536750525.441 * * [misc]simplify: iters left: 3 (83 enodes) 1536750525.481 * * [misc]simplify: iters left: 2 (218 enodes) 1536750525.759 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (+ (log PI) (log n)) (log 2))) (log (sqrt k))) 1536750525.759 * [misc]simplify: Simplified (2 1) to (λ (k n) (exp (- (* (- 1/2 (/ k 2)) (+ (+ (log PI) (log n)) (log 2))) (log (sqrt k))))) 1536750525.759 * * * * [misc]progress: [ 30 / 144 ] simplifiying candidate # 1536750525.759 * * * * [misc]progress: [ 31 / 144 ] simplifiying candidate # 1536750525.759 * * * * [misc]progress: [ 32 / 144 ] simplifiying candidate # 1536750525.759 * [enter]simplify: Simplifying (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))))) 1536750525.761 * * [misc]simplify: iters left: 6 (22 enodes) 1536750525.767 * * [misc]simplify: iters left: 5 (45 enodes) 1536750525.786 * * [misc]simplify: iters left: 4 (167 enodes) 1536750526.111 * [exit]simplify: Simplified to (/ (* (pow (pow n (- 1/2 (/ k 2))) 3) (pow (pow 2 (- 1/2 (/ k 2))) 3)) (/ (/ (* k (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))))) 1536750526.111 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (/ (* (pow (pow n (- 1/2 (/ k 2))) 3) (pow (pow 2 (- 1/2 (/ k 2))) 3)) (/ (/ (* k (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))))))) 1536750526.111 * * * * [misc]progress: [ 33 / 144 ] simplifiying candidate # 1536750526.111 * [enter]simplify: Simplifying (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (* (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536750526.112 * * [misc]simplify: iters left: 6 (20 enodes) 1536750526.120 * * [misc]simplify: iters left: 5 (41 enodes) 1536750526.150 * * [misc]simplify: iters left: 4 (140 enodes) 1536750526.300 * [exit]simplify: Simplified to (* (* (pow (pow n (- 1/2 (/ k 2))) 3) (pow (pow 2 (- 1/2 (/ k 2))) 3)) (pow (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 3)) 1536750526.300 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (pow n (- 1/2 (/ k 2))) 3) (pow (pow 2 (- 1/2 (/ k 2))) 3)) (pow (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 3)))) 1536750526.300 * * * * [misc]progress: [ 34 / 144 ] simplifiying candidate # 1536750526.300 * [enter]simplify: Simplifying (* (* (* (pow 2 (- 1/2 (/ k 2))) (pow 2 (- 1/2 (/ k 2)))) (pow 2 (- 1/2 (/ k 2)))) (* (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536750526.302 * * [misc]simplify: iters left: 6 (18 enodes) 1536750526.306 * * [misc]simplify: iters left: 5 (36 enodes) 1536750526.320 * * [misc]simplify: iters left: 4 (116 enodes) 1536750526.399 * * [misc]simplify: iters left: 3 (465 enodes) 1536750527.241 * [exit]simplify: Simplified to (* (* (pow (pow 2 (- 1/2 (/ k 2))) 3) (pow (pow n (- 1/2 (/ k 2))) 3)) (pow (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 3)) 1536750527.241 * [misc]simplify: Simplified (2 1) to (λ (k n) (cbrt (* (* (pow (pow 2 (- 1/2 (/ k 2))) 3) (pow (pow n (- 1/2 (/ k 2))) 3)) (pow (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 3)))) 1536750527.241 * * * * [misc]progress: [ 35 / 144 ] simplifiying candidate # 1536750527.241 * * * * [misc]progress: [ 36 / 144 ] simplifiying candidate # 1536750527.241 * * * * [misc]progress: [ 37 / 144 ] simplifiying candidate # 1536750527.241 * * * * [misc]progress: [ 38 / 144 ] simplifiying candidate # 1536750527.241 * [enter]simplify: Simplifying (* (pow 2 1/2) (* (pow n 1/2) (pow PI (- 1/2 (/ k 2))))) 1536750527.242 * * [misc]simplify: iters left: 6 (12 enodes) 1536750527.246 * * [misc]simplify: iters left: 5 (20 enodes) 1536750527.251 * * [misc]simplify: iters left: 4 (29 enodes) 1536750527.256 * * [misc]simplify: iters left: 3 (30 enodes) 1536750527.261 * [exit]simplify: Simplified to (* (* (sqrt n) (sqrt 2)) (pow PI (- 1/2 (/ k 2)))) 1536750527.261 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (* (sqrt n) (sqrt 2)) (pow PI (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (* (pow n (/ k 2)) (sqrt k))))) 1536750527.261 * [enter]simplify: Simplifying (* (pow 2 (/ k 2)) (* (pow n (/ k 2)) (sqrt k))) 1536750527.262 * * [misc]simplify: iters left: 6 (9 enodes) 1536750527.264 * * [misc]simplify: iters left: 5 (13 enodes) 1536750527.266 * * [misc]simplify: iters left: 4 (19 enodes) 1536750527.269 * * [misc]simplify: iters left: 3 (21 enodes) 1536750527.274 * [exit]simplify: Simplified to (* (pow 2 (/ k 2)) (* (pow n (/ k 2)) (sqrt k))) 1536750527.275 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (* (sqrt n) (sqrt 2)) (pow PI (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (* (pow n (/ k 2)) (sqrt k))))) 1536750527.275 * * * * [misc]progress: [ 39 / 144 ] simplifiying candidate # 1536750527.275 * [enter]simplify: Simplifying (* (pow 2 1/2) (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2))))) 1536750527.275 * * [misc]simplify: iters left: 6 (12 enodes) 1536750527.279 * * [misc]simplify: iters left: 5 (19 enodes) 1536750527.284 * * [misc]simplify: iters left: 4 (28 enodes) 1536750527.289 * * [misc]simplify: iters left: 3 (30 enodes) 1536750527.295 * [exit]simplify: Simplified to (* (* (sqrt 2) (pow PI (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) 1536750527.295 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (* (sqrt 2) (pow PI (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (sqrt k)))) 1536750527.295 * [enter]simplify: Simplifying (* (pow 2 (/ k 2)) (sqrt k)) 1536750527.295 * * [misc]simplify: iters left: 5 (6 enodes) 1536750527.296 * * [misc]simplify: iters left: 4 (7 enodes) 1536750527.298 * [exit]simplify: Simplified to (* (pow 2 (/ k 2)) (sqrt k)) 1536750527.298 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (* (sqrt 2) (pow PI (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (* (pow 2 (/ k 2)) (sqrt k)))) 1536750527.298 * * * * [misc]progress: [ 40 / 144 ] simplifiying candidate # 1536750527.298 * [enter]simplify: Simplifying (* (pow 2 1/2) (* (pow n 1/2) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) 1536750527.299 * * [misc]simplify: iters left: 6 (14 enodes) 1536750527.302 * * [misc]simplify: iters left: 5 (24 enodes) 1536750527.309 * * [misc]simplify: iters left: 4 (43 enodes) 1536750527.317 * * [misc]simplify: iters left: 3 (60 enodes) 1536750527.335 * * [misc]simplify: iters left: 2 (74 enodes) 1536750527.361 * * [misc]simplify: iters left: 1 (97 enodes) 1536750527.406 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (* (sqrt n) (sqrt 2)))) 1536750527.406 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (* (sqrt n) (sqrt 2)))) (* (pow 2 (/ k 2)) (pow n (/ k 2))))) 1536750527.406 * [enter]simplify: Simplifying (* (pow 2 (/ k 2)) (pow n (/ k 2))) 1536750527.407 * * [misc]simplify: iters left: 5 (7 enodes) 1536750527.409 * * [misc]simplify: iters left: 4 (8 enodes) 1536750527.412 * [exit]simplify: Simplified to (* (pow 2 (/ k 2)) (pow n (/ k 2))) 1536750527.412 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (/ (pow PI (- 1/2 (/ k 2))) (/ (sqrt k) (* (sqrt n) (sqrt 2)))) (* (pow 2 (/ k 2)) (pow n (/ k 2))))) 1536750527.412 * * * * [misc]progress: [ 41 / 144 ] simplifiying candidate # 1536750527.412 * * * * [misc]progress: [ 42 / 144 ] simplifiying candidate # 1536750527.413 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536750527.414 * * [misc]simplify: iters left: 6 (9 enodes) 1536750527.417 * * [misc]simplify: iters left: 5 (11 enodes) 1536750527.421 * * [misc]simplify: iters left: 4 (14 enodes) 1536750527.425 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536750527.425 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (* (pow 2 (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) 1536750527.425 * * * * [misc]progress: [ 43 / 144 ] simplifiying candidate # 1536750527.426 * [enter]simplify: Simplifying (pow 2 1/2) 1536750527.426 * * [misc]simplify: iters left: 1 (3 enodes) 1536750527.428 * [exit]simplify: Simplified to (sqrt 2) 1536750527.428 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt 2) (* (pow 2 (- (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536750527.428 * * * * [misc]progress: [ 44 / 144 ] simplifiying candidate # 1536750527.429 * [enter]simplify: Simplifying (pow 2 1/2) 1536750527.429 * * [misc]simplify: iters left: 1 (3 enodes) 1536750527.431 * [exit]simplify: Simplified to (sqrt 2) 1536750527.431 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt 2) (* (pow 2 (- (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536750527.431 * * * * [misc]progress: [ 45 / 144 ] simplifiying candidate # 1536750527.432 * [enter]simplify: Simplifying (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) 1536750527.432 * * [misc]simplify: iters left: 6 (8 enodes) 1536750527.435 * * [misc]simplify: iters left: 5 (10 enodes) 1536750527.439 * * [misc]simplify: iters left: 4 (13 enodes) 1536750527.452 * [exit]simplify: Simplified to (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) 1536750527.452 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (cbrt (pow 2 (- 1/2 (/ k 2))))) (* (cbrt (pow 2 (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536750527.452 * * * * [misc]progress: [ 46 / 144 ] simplifiying candidate # 1536750527.452 * [enter]simplify: Simplifying (sqrt (pow 2 (- 1/2 (/ k 2)))) 1536750527.453 * * [misc]simplify: iters left: 6 (7 enodes) 1536750527.456 * * [misc]simplify: iters left: 5 (9 enodes) 1536750527.459 * * [misc]simplify: iters left: 4 (12 enodes) 1536750527.463 * [exit]simplify: Simplified to (sqrt (pow 2 (- 1/2 (/ k 2)))) 1536750527.463 * [misc]simplify: Simplified (2 1) to (λ (k n) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (sqrt (pow 2 (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536750527.463 * * * * [misc]progress: [ 47 / 144 ] simplifiying candidate # 1536750527.463 * * * * [misc]progress: [ 48 / 144 ] simplifiying candidate # 1536750527.463 * [enter]simplify: Simplifying (* (pow n (/ k 2)) (sqrt k)) 1536750527.464 * * [misc]simplify: iters left: 5 (7 enodes) 1536750527.467 * * [misc]simplify: iters left: 4 (8 enodes) 1536750527.469 * [exit]simplify: Simplified to (* (pow n (/ k 2)) (sqrt k)) 1536750527.470 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow n 1/2) (pow PI (- 1/2 (/ k 2))))) (* (pow n (/ k 2)) (sqrt k)))) 1536750527.470 * * * * [misc]progress: [ 49 / 144 ] simplifiying candidate # 1536750527.470 * [enter]simplify: Simplifying (sqrt k) 1536750527.470 * * [misc]simplify: iters left: 1 (2 enodes) 1536750527.471 * [exit]simplify: Simplified to (sqrt k) 1536750527.471 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2))))) (sqrt k))) 1536750527.471 * * * * [misc]progress: [ 50 / 144 ] simplifiying candidate # 1536750527.471 * [enter]simplify: Simplifying (pow n (/ k 2)) 1536750527.471 * * [misc]simplify: iters left: 3 (5 enodes) 1536750527.473 * [exit]simplify: Simplified to (pow n (/ k 2)) 1536750527.473 * [misc]simplify: Simplified (2 2) to (λ (k n) (/ (* (pow 2 (- 1/2 (/ k 2))) (* (pow n 1/2) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (pow n (/ k 2)))) 1536750527.473 * * * * [misc]progress: [ 51 / 144 ] simplifiying candidate # 1536750527.473 * [enter]simplify: Simplifying (* (pow 2 1/2) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) 1536750527.475 * * [misc]simplify: iters left: 6 (14 enodes) 1536750527.482 * * [misc]simplify: iters left: 5 (23 enodes) 1536750527.493 * * [misc]simplify: iters left: 4 (42 enodes) 1536750527.510 * * [misc]simplify: iters left: 3 (59 enodes) 1536750527.531 * * [misc]simplify: iters left: 2 (73 enodes) 1536750527.559 * * [misc]simplify: iters left: 1 (96 enodes) 1536750527.589 * [exit]simplify: Simplified to (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (* (pow n (- 1/2 (/ k 2))) (sqrt 2))) 1536750527.589 * [misc]simplify: Simplified (2 1) to (λ (k n) (/ (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (* (pow n (- 1/2 (/ k 2))) (sqrt 2))) (pow 2 (/ k 2)))) 1536750527.589 * * * * [misc]progress: [ 52 / 144 ] simplifiying candidate # 1536750527.589 * * * * [misc]progress: [ 53 / 144 ] simplifiying candidate # 1536750527.589 * * * * [misc]progress: [ 54 / 144 ] simplifiying candidate # 1536750527.589 * [enter]simplify: Simplifying (+ (* (log n) (- 1/2 (/ k 2))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))) 1536750527.590 * * [misc]simplify: iters left: 6 (15 enodes) 1536750527.593 * * [misc]simplify: iters left: 5 (24 enodes) 1536750527.599 * * [misc]simplify: iters left: 4 (48 enodes) 1536750527.630 * * [misc]simplify: iters left: 3 (126 enodes) 1536750527.677 * * [misc]simplify: iters left: 2 (346 enodes) 1536750527.983 * [exit]simplify: Simplified to (- (* (+ (log PI) (log n)) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750527.984 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (+ (log PI) (log n)) (- 1/2 (/ k 2))) (log (sqrt k)))))) 1536750527.984 * * * * [misc]progress: [ 55 / 144 ] simplifiying candidate # 1536750527.984 * [enter]simplify: Simplifying (+ (* (log n) (- 1/2 (/ k 2))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))) 1536750527.985 * * [misc]simplify: iters left: 6 (15 enodes) 1536750527.988 * * [misc]simplify: iters left: 5 (25 enodes) 1536750527.994 * * [misc]simplify: iters left: 4 (44 enodes) 1536750528.007 * * [misc]simplify: iters left: 3 (95 enodes) 1536750528.072 * * [misc]simplify: iters left: 2 (273 enodes) 1536750528.353 * [exit]simplify: Simplified to (- (* (+ (log PI) (log n)) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750528.353 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (+ (log PI) (log n)) (- 1/2 (/ k 2))) (log (sqrt k)))))) 1536750528.353 * * * * [misc]progress: [ 56 / 144 ] simplifiying candidate # 1536750528.353 * [enter]simplify: Simplifying (+ (* (log n) (- 1/2 (/ k 2))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) 1536750528.354 * * [misc]simplify: iters left: 6 (14 enodes) 1536750528.357 * * [misc]simplify: iters left: 5 (21 enodes) 1536750528.362 * * [misc]simplify: iters left: 4 (38 enodes) 1536750528.372 * * [misc]simplify: iters left: 3 (76 enodes) 1536750528.395 * * [misc]simplify: iters left: 2 (166 enodes) 1536750528.506 * * [misc]simplify: iters left: 1 (420 enodes) 1536750528.866 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k))) 1536750528.866 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k)))))) 1536750528.866 * * * * [misc]progress: [ 57 / 144 ] simplifiying candidate # 1536750528.866 * [enter]simplify: Simplifying (+ (log (pow n (- 1/2 (/ k 2)))) (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k)))) 1536750528.867 * * [misc]simplify: iters left: 6 (15 enodes) 1536750528.870 * * [misc]simplify: iters left: 5 (25 enodes) 1536750528.881 * * [misc]simplify: iters left: 4 (44 enodes) 1536750528.905 * * [misc]simplify: iters left: 3 (95 enodes) 1536750528.950 * * [misc]simplify: iters left: 2 (271 enodes) 1536750529.164 * [exit]simplify: Simplified to (- (* (+ (log PI) (log n)) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750529.164 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (+ (log PI) (log n)) (- 1/2 (/ k 2))) (log (sqrt k)))))) 1536750529.164 * * * * [misc]progress: [ 58 / 144 ] simplifiying candidate # 1536750529.164 * [enter]simplify: Simplifying (+ (log (pow n (- 1/2 (/ k 2)))) (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k)))) 1536750529.166 * * [misc]simplify: iters left: 6 (15 enodes) 1536750529.172 * * [misc]simplify: iters left: 5 (26 enodes) 1536750529.183 * * [misc]simplify: iters left: 4 (40 enodes) 1536750529.192 * * [misc]simplify: iters left: 3 (66 enodes) 1536750529.226 * * [misc]simplify: iters left: 2 (230 enodes) 1536750529.409 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k))) 1536750529.409 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k)))))) 1536750529.409 * * * * [misc]progress: [ 59 / 144 ] simplifiying candidate # 1536750529.409 * [enter]simplify: Simplifying (+ (log (pow n (- 1/2 (/ k 2)))) (log (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) 1536750529.410 * * [misc]simplify: iters left: 6 (14 enodes) 1536750529.413 * * [misc]simplify: iters left: 5 (22 enodes) 1536750529.417 * * [misc]simplify: iters left: 4 (34 enodes) 1536750529.424 * * [misc]simplify: iters left: 3 (54 enodes) 1536750529.444 * * [misc]simplify: iters left: 2 (145 enodes) 1536750529.564 * * [misc]simplify: iters left: 1 (442 enodes) 1536750530.103 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k))) 1536750530.103 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (+ (log n) (log PI))) (log (sqrt k)))))) 1536750530.103 * * * * [misc]progress: [ 60 / 144 ] simplifiying candidate # 1536750530.103 * * * * [misc]progress: [ 61 / 144 ] simplifiying candidate # 1536750530.103 * * * * [misc]progress: [ 62 / 144 ] simplifiying candidate # 1536750530.104 * [enter]simplify: Simplifying (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))) 1536750530.106 * * [misc]simplify: iters left: 6 (18 enodes) 1536750530.115 * * [misc]simplify: iters left: 5 (35 enodes) 1536750530.139 * * [misc]simplify: iters left: 4 (111 enodes) 1536750530.257 * * [misc]simplify: iters left: 3 (435 enodes) 1536750530.963 * [exit]simplify: Simplified to (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2))))) (/ (/ (* k (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2))))) 1536750530.963 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (cbrt (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2))))) (/ (/ (* k (sqrt k)) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))))))) 1536750530.963 * * * * [misc]progress: [ 63 / 144 ] simplifiying candidate # 1536750530.964 * [enter]simplify: Simplifying (* (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2)))) (* (* (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) 1536750530.965 * * [misc]simplify: iters left: 6 (16 enodes) 1536750530.969 * * [misc]simplify: iters left: 5 (31 enodes) 1536750530.987 * * [misc]simplify: iters left: 4 (89 enodes) 1536750531.051 * * [misc]simplify: iters left: 3 (229 enodes) 1536750531.307 * [exit]simplify: Simplified to (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2))))) (* (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))) (/ k (pow PI (- 1/2 (/ k 2)))))) 1536750531.307 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (cbrt (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2))))) (* (/ (sqrt k) (pow PI (- 1/2 (/ k 2)))) (/ k (pow PI (- 1/2 (/ k 2))))))))) 1536750531.307 * * * * [misc]progress: [ 64 / 144 ] simplifiying candidate # 1536750531.307 * * * * [misc]progress: [ 65 / 144 ] simplifiying candidate # 1536750531.307 * * * * [misc]progress: [ 66 / 144 ] simplifiying candidate # 1536750531.307 * * * * [misc]progress: [ 67 / 144 ] simplifiying candidate # 1536750531.308 * [enter]simplify: Simplifying (* (pow n 1/2) (pow PI (- 1/2 (/ k 2)))) 1536750531.309 * * [misc]simplify: iters left: 6 (10 enodes) 1536750531.312 * * [misc]simplify: iters left: 5 (14 enodes) 1536750531.317 * * [misc]simplify: iters left: 4 (17 enodes) 1536750531.323 * [exit]simplify: Simplified to (* (sqrt n) (pow PI (- 1/2 (/ k 2)))) 1536750531.323 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (sqrt n) (pow PI (- 1/2 (/ k 2)))) (* (pow n (/ k 2)) (sqrt k))))) 1536750531.323 * [enter]simplify: Simplifying (* (pow n (/ k 2)) (sqrt k)) 1536750531.324 * * [misc]simplify: iters left: 5 (7 enodes) 1536750531.326 * * [misc]simplify: iters left: 4 (8 enodes) 1536750531.329 * [exit]simplify: Simplified to (* (pow n (/ k 2)) (sqrt k)) 1536750531.329 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (sqrt n) (pow PI (- 1/2 (/ k 2)))) (* (pow n (/ k 2)) (sqrt k))))) 1536750531.329 * * * * [misc]progress: [ 68 / 144 ] simplifiying candidate # 1536750531.329 * * * * [misc]progress: [ 69 / 144 ] simplifiying candidate # 1536750531.330 * [enter]simplify: Simplifying (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) 1536750531.330 * * [misc]simplify: iters left: 6 (10 enodes) 1536750531.334 * * [misc]simplify: iters left: 5 (12 enodes) 1536750531.338 * * [misc]simplify: iters left: 4 (15 enodes) 1536750531.344 * [exit]simplify: Simplified to (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) 1536750531.344 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (* (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536750531.344 * * * * [misc]progress: [ 70 / 144 ] simplifiying candidate # 1536750531.344 * [enter]simplify: Simplifying (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) 1536750531.345 * * [misc]simplify: iters left: 6 (10 enodes) 1536750531.349 * * [misc]simplify: iters left: 5 (12 enodes) 1536750531.353 * * [misc]simplify: iters left: 4 (15 enodes) 1536750531.358 * [exit]simplify: Simplified to (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) 1536750531.358 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536750531.358 * * * * [misc]progress: [ 71 / 144 ] simplifiying candidate # 1536750531.358 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (cbrt (sqrt k))) 1536750531.359 * * [misc]simplify: iters left: 6 (9 enodes) 1536750531.362 * * [misc]simplify: iters left: 5 (11 enodes) 1536750531.366 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k))) 1536750531.366 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k)))))) 1536750531.366 * * * * [misc]progress: [ 72 / 144 ] simplifiying candidate # 1536750531.367 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))) 1536750531.369 * * [misc]simplify: iters left: 6 (9 enodes) 1536750531.372 * * [misc]simplify: iters left: 5 (11 enodes) 1536750531.376 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))) 1536750531.376 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (sqrt (sqrt k)))) (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k)))))) 1536750531.376 * * * * [misc]progress: [ 73 / 144 ] simplifiying candidate # 1536750531.377 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt k)) 1536750531.377 * * [misc]simplify: iters left: 6 (8 enodes) 1536750531.380 * * [misc]simplify: iters left: 5 (10 enodes) 1536750531.384 * [exit]simplify: Simplified to (/ (pow PI (- (/ k 2))) (sqrt k)) 1536750531.384 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) 1)) (/ (pow PI (- (/ k 2))) (sqrt k))))) 1536750531.384 * * * * [misc]progress: [ 74 / 144 ] simplifiying candidate # 1536750531.384 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (cbrt (sqrt k))) 1536750531.385 * * [misc]simplify: iters left: 6 (9 enodes) 1536750531.388 * * [misc]simplify: iters left: 5 (11 enodes) 1536750531.392 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k))) 1536750531.392 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k)))))) 1536750531.392 * * * * [misc]progress: [ 75 / 144 ] simplifiying candidate # 1536750531.393 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))) 1536750531.394 * * [misc]simplify: iters left: 6 (9 enodes) 1536750531.397 * * [misc]simplify: iters left: 5 (11 enodes) 1536750531.400 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))) 1536750531.401 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) (sqrt (sqrt k)))) (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k)))))) 1536750531.401 * * * * [misc]progress: [ 76 / 144 ] simplifiying candidate # 1536750531.401 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt k)) 1536750531.402 * * [misc]simplify: iters left: 6 (8 enodes) 1536750531.405 * * [misc]simplify: iters left: 5 (10 enodes) 1536750531.409 * [exit]simplify: Simplified to (/ (pow PI (- (/ k 2))) (sqrt k)) 1536750531.409 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (pow PI 1/2) 1)) (/ (pow PI (- (/ k 2))) (sqrt k))))) 1536750531.409 * * * * [misc]progress: [ 77 / 144 ] simplifiying candidate # 1536750531.409 * [enter]simplify: Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750531.410 * * [misc]simplify: iters left: 6 (11 enodes) 1536750531.414 * * [misc]simplify: iters left: 5 (13 enodes) 1536750531.418 * * [misc]simplify: iters left: 4 (16 enodes) 1536750531.423 * [exit]simplify: Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750531.424 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1536750531.424 * * * * [misc]progress: [ 78 / 144 ] simplifiying candidate # 1536750531.424 * [enter]simplify: Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750531.425 * * [misc]simplify: iters left: 6 (11 enodes) 1536750531.429 * * [misc]simplify: iters left: 5 (13 enodes) 1536750531.433 * * [misc]simplify: iters left: 4 (16 enodes) 1536750531.438 * [exit]simplify: Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750531.438 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1536750531.439 * * * * [misc]progress: [ 79 / 144 ] simplifiying candidate # 1536750531.439 * [enter]simplify: Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536750531.440 * * [misc]simplify: iters left: 6 (10 enodes) 1536750531.443 * * [misc]simplify: iters left: 5 (12 enodes) 1536750531.447 * * [misc]simplify: iters left: 4 (15 enodes) 1536750531.452 * [exit]simplify: Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536750531.452 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1)) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))))) 1536750531.452 * * * * [misc]progress: [ 80 / 144 ] simplifiying candidate # 1536750531.453 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750531.454 * * [misc]simplify: iters left: 6 (11 enodes) 1536750531.457 * * [misc]simplify: iters left: 5 (13 enodes) 1536750531.462 * * [misc]simplify: iters left: 4 (16 enodes) 1536750531.467 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750531.467 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))) 1536750531.467 * * * * [misc]progress: [ 81 / 144 ] simplifiying candidate # 1536750531.467 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750531.469 * * [misc]simplify: iters left: 6 (11 enodes) 1536750531.472 * * [misc]simplify: iters left: 5 (13 enodes) 1536750531.477 * * [misc]simplify: iters left: 4 (16 enodes) 1536750531.482 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750531.483 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))) 1536750531.483 * * * * [misc]progress: [ 82 / 144 ] simplifiying candidate # 1536750531.483 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536750531.484 * * [misc]simplify: iters left: 6 (10 enodes) 1536750531.487 * * [misc]simplify: iters left: 5 (12 enodes) 1536750531.491 * * [misc]simplify: iters left: 4 (15 enodes) 1536750531.496 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536750531.496 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) 1)) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k))))) 1536750531.496 * * * * [misc]progress: [ 83 / 144 ] simplifiying candidate # 1536750531.497 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750531.498 * * [misc]simplify: iters left: 6 (10 enodes) 1536750531.501 * * [misc]simplify: iters left: 5 (12 enodes) 1536750531.507 * * [misc]simplify: iters left: 4 (15 enodes) 1536750531.512 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750531.512 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))) 1536750531.512 * * * * [misc]progress: [ 84 / 144 ] simplifiying candidate # 1536750531.512 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750531.513 * * [misc]simplify: iters left: 6 (10 enodes) 1536750531.517 * * [misc]simplify: iters left: 5 (12 enodes) 1536750531.521 * * [misc]simplify: iters left: 4 (15 enodes) 1536750531.525 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750531.525 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ 1 (sqrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))) 1536750531.525 * * * * [misc]progress: [ 85 / 144 ] simplifiying candidate # 1536750531.525 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536750531.525 * * [misc]simplify: iters left: 6 (9 enodes) 1536750531.527 * * [misc]simplify: iters left: 5 (11 enodes) 1536750531.529 * * [misc]simplify: iters left: 4 (14 enodes) 1536750531.531 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536750531.531 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (/ 1 1)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536750531.532 * * * * [misc]progress: [ 86 / 144 ] simplifiying candidate # 1536750531.532 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536750531.532 * * [misc]simplify: iters left: 6 (9 enodes) 1536750531.534 * * [misc]simplify: iters left: 5 (11 enodes) 1536750531.536 * * [misc]simplify: iters left: 4 (14 enodes) 1536750531.538 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536750531.538 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) 1) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))) 1536750531.538 * * * * [misc]progress: [ 87 / 144 ] simplifiying candidate # 1536750531.538 * [enter]simplify: Simplifying (/ 1 (sqrt k)) 1536750531.538 * * [misc]simplify: iters left: 3 (4 enodes) 1536750531.539 * * [misc]simplify: iters left: 2 (6 enodes) 1536750531.540 * [exit]simplify: Simplified to (/ 1 (sqrt k)) 1536750531.540 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (/ 1 (sqrt k))))) 1536750531.540 * * * * [misc]progress: [ 88 / 144 ] simplifiying candidate # 1536750531.540 * [enter]simplify: Simplifying (pow n 1/2) 1536750531.540 * * [misc]simplify: iters left: 1 (3 enodes) 1536750531.541 * [exit]simplify: Simplified to (sqrt n) 1536750531.541 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt n) (* (pow n (- (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536750531.541 * * * * [misc]progress: [ 89 / 144 ] simplifiying candidate # 1536750531.541 * [enter]simplify: Simplifying (pow n 1/2) 1536750531.541 * * [misc]simplify: iters left: 1 (3 enodes) 1536750531.542 * [exit]simplify: Simplified to (sqrt n) 1536750531.542 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt n) (* (pow n (- (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536750531.542 * * * * [misc]progress: [ 90 / 144 ] simplifiying candidate # 1536750531.542 * [enter]simplify: Simplifying (* (cbrt (pow n (- 1/2 (/ k 2)))) (cbrt (pow n (- 1/2 (/ k 2))))) 1536750531.542 * * [misc]simplify: iters left: 6 (9 enodes) 1536750531.544 * * [misc]simplify: iters left: 5 (11 enodes) 1536750531.546 * * [misc]simplify: iters left: 4 (14 enodes) 1536750531.548 * [exit]simplify: Simplified to (* (cbrt (pow n (- 1/2 (/ k 2)))) (cbrt (pow n (- 1/2 (/ k 2))))) 1536750531.548 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (* (cbrt (pow n (- 1/2 (/ k 2)))) (cbrt (pow n (- 1/2 (/ k 2))))) (* (cbrt (pow n (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536750531.548 * * * * [misc]progress: [ 91 / 144 ] simplifiying candidate # 1536750531.548 * [enter]simplify: Simplifying (sqrt (pow n (- 1/2 (/ k 2)))) 1536750531.549 * * [misc]simplify: iters left: 6 (8 enodes) 1536750531.550 * * [misc]simplify: iters left: 5 (10 enodes) 1536750531.552 * * [misc]simplify: iters left: 4 (13 enodes) 1536750531.554 * [exit]simplify: Simplified to (sqrt (pow n (- 1/2 (/ k 2)))) 1536750531.554 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (sqrt (pow n (- 1/2 (/ k 2)))) (* (sqrt (pow n (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536750531.554 * * * * [misc]progress: [ 92 / 144 ] simplifiying candidate # 1536750531.554 * * * * [misc]progress: [ 93 / 144 ] simplifiying candidate # 1536750531.554 * [enter]simplify: Simplifying (sqrt k) 1536750531.554 * * [misc]simplify: iters left: 1 (2 enodes) 1536750531.555 * [exit]simplify: Simplified to (sqrt k) 1536750531.555 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow n (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k)))) 1536750531.555 * * * * [misc]progress: [ 94 / 144 ] simplifiying candidate # 1536750531.555 * [enter]simplify: Simplifying (* (pow n 1/2) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) 1536750531.555 * * [misc]simplify: iters left: 6 (12 enodes) 1536750531.558 * * [misc]simplify: iters left: 5 (18 enodes) 1536750531.561 * * [misc]simplify: iters left: 4 (25 enodes) 1536750531.566 * * [misc]simplify: iters left: 3 (27 enodes) 1536750531.573 * * [misc]simplify: iters left: 2 (29 enodes) 1536750531.581 * * [misc]simplify: iters left: 1 (30 enodes) 1536750531.591 * [exit]simplify: Simplified to (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt n) (sqrt k))) 1536750531.591 * [misc]simplify: Simplified (2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (/ (* (pow PI (- 1/2 (/ k 2))) (/ (sqrt n) (sqrt k))) (pow n (/ k 2))))) 1536750531.591 * * * * [misc]progress: [ 95 / 144 ] simplifiying candidate # 1536750531.591 * * * * [misc]progress: [ 96 / 144 ] simplifiying candidate # 1536750531.592 * * * * [misc]progress: [ 97 / 144 ] simplifiying candidate # 1536750531.592 * [enter]simplify: Simplifying (- (* (log PI) (- 1/2 (/ k 2))) (log (sqrt k))) 1536750531.593 * * [misc]simplify: iters left: 6 (11 enodes) 1536750531.597 * * [misc]simplify: iters left: 5 (16 enodes) 1536750531.603 * * [misc]simplify: iters left: 4 (26 enodes) 1536750531.617 * * [misc]simplify: iters left: 3 (48 enodes) 1536750531.637 * * [misc]simplify: iters left: 2 (84 enodes) 1536750531.667 * * [misc]simplify: iters left: 1 (110 enodes) 1536750531.703 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log PI)) (log (sqrt k))) 1536750531.704 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (log PI)) (log (sqrt k))))))) 1536750531.704 * * * * [misc]progress: [ 98 / 144 ] simplifiying candidate # 1536750531.704 * [enter]simplify: Simplifying (- (log (pow PI (- 1/2 (/ k 2)))) (log (sqrt k))) 1536750531.704 * * [misc]simplify: iters left: 6 (11 enodes) 1536750531.707 * * [misc]simplify: iters left: 5 (17 enodes) 1536750531.709 * * [misc]simplify: iters left: 4 (22 enodes) 1536750531.713 * * [misc]simplify: iters left: 3 (30 enodes) 1536750531.721 * * [misc]simplify: iters left: 2 (62 enodes) 1536750531.738 * * [misc]simplify: iters left: 1 (115 enodes) 1536750531.787 * [exit]simplify: Simplified to (- (* (- 1/2 (/ k 2)) (log PI)) (log (sqrt k))) 1536750531.787 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (exp (- (* (- 1/2 (/ k 2)) (log PI)) (log (sqrt k))))))) 1536750531.787 * * * * [misc]progress: [ 99 / 144 ] simplifiying candidate # 1536750531.787 * * * * [misc]progress: [ 100 / 144 ] simplifiying candidate # 1536750531.787 * * * * [misc]progress: [ 101 / 144 ] simplifiying candidate # 1536750531.787 * [enter]simplify: Simplifying (/ (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (pow PI (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) 1536750531.789 * * [misc]simplify: iters left: 6 (13 enodes) 1536750531.795 * * [misc]simplify: iters left: 5 (24 enodes) 1536750531.808 * * [misc]simplify: iters left: 4 (55 enodes) 1536750531.835 * * [misc]simplify: iters left: 3 (110 enodes) 1536750531.874 * * [misc]simplify: iters left: 2 (193 enodes) 1536750531.955 * * [misc]simplify: iters left: 1 (324 enodes) 1536750532.178 * [exit]simplify: Simplified to (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (* (sqrt k) k))) 1536750532.179 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (cbrt (* (* (pow PI (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (/ (pow PI (- 1/2 (/ k 2))) (* (sqrt k) k))))))) 1536750532.179 * * * * [misc]progress: [ 102 / 144 ] simplifiying candidate # 1536750532.179 * * * * [misc]progress: [ 103 / 144 ] simplifiying candidate # 1536750532.179 * * * * [misc]progress: [ 104 / 144 ] simplifiying candidate # 1536750532.179 * * * * [misc]progress: [ 105 / 144 ] simplifiying candidate # 1536750532.179 * * * * [misc]progress: [ 106 / 144 ] simplifiying candidate # 1536750532.179 * [enter]simplify: Simplifying (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750532.180 * * [misc]simplify: iters left: 6 (8 enodes) 1536750532.181 * * [misc]simplify: iters left: 5 (11 enodes) 1536750532.183 * [exit]simplify: Simplified to (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) 1536750532.183 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow PI (- (/ k 2))) (cbrt (sqrt k))))))) 1536750532.184 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (cbrt (sqrt k))) 1536750532.184 * * [misc]simplify: iters left: 6 (9 enodes) 1536750532.186 * * [misc]simplify: iters left: 5 (11 enodes) 1536750532.188 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k))) 1536750532.188 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k))))))) 1536750532.188 * * * * [misc]progress: [ 107 / 144 ] simplifiying candidate # 1536750532.188 * [enter]simplify: Simplifying (/ (pow PI 1/2) (sqrt (sqrt k))) 1536750532.188 * * [misc]simplify: iters left: 4 (7 enodes) 1536750532.192 * * [misc]simplify: iters left: 3 (8 enodes) 1536750532.193 * [exit]simplify: Simplified to (/ (sqrt PI) (sqrt (sqrt k))) 1536750532.193 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt PI) (sqrt (sqrt k))) (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))))))) 1536750532.193 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))) 1536750532.194 * * [misc]simplify: iters left: 6 (9 enodes) 1536750532.195 * * [misc]simplify: iters left: 5 (11 enodes) 1536750532.197 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))) 1536750532.197 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt PI) (sqrt (sqrt k))) (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))))))) 1536750532.197 * * * * [misc]progress: [ 108 / 144 ] simplifiying candidate # 1536750532.197 * [enter]simplify: Simplifying (/ (pow PI 1/2) 1) 1536750532.198 * * [misc]simplify: iters left: 3 (5 enodes) 1536750532.199 * * [misc]simplify: iters left: 2 (8 enodes) 1536750532.200 * * [misc]simplify: iters left: 1 (10 enodes) 1536750532.201 * [exit]simplify: Simplified to (sqrt PI) 1536750532.202 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt PI) (/ (pow PI (- (/ k 2))) (sqrt k)))))) 1536750532.202 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt k)) 1536750532.202 * * [misc]simplify: iters left: 6 (8 enodes) 1536750532.204 * * [misc]simplify: iters left: 5 (10 enodes) 1536750532.207 * [exit]simplify: Simplified to (/ (pow PI (- (/ k 2))) (sqrt k)) 1536750532.207 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt PI) (/ (pow PI (- (/ k 2))) (sqrt k)))))) 1536750532.208 * * * * [misc]progress: [ 109 / 144 ] simplifiying candidate # 1536750532.208 * [enter]simplify: Simplifying (/ (pow PI 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750532.209 * * [misc]simplify: iters left: 6 (8 enodes) 1536750532.212 * * [misc]simplify: iters left: 5 (11 enodes) 1536750532.216 * [exit]simplify: Simplified to (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) 1536750532.216 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow PI (- (/ k 2))) (cbrt (sqrt k))))))) 1536750532.216 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (cbrt (sqrt k))) 1536750532.217 * * [misc]simplify: iters left: 6 (9 enodes) 1536750532.220 * * [misc]simplify: iters left: 5 (11 enodes) 1536750532.225 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k))) 1536750532.225 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (/ (sqrt PI) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow PI (/ (- k) 2)) (cbrt (sqrt k))))))) 1536750532.225 * * * * [misc]progress: [ 110 / 144 ] simplifiying candidate # 1536750532.225 * [enter]simplify: Simplifying (/ (pow PI 1/2) (sqrt (sqrt k))) 1536750532.226 * * [misc]simplify: iters left: 4 (7 enodes) 1536750532.228 * * [misc]simplify: iters left: 3 (8 enodes) 1536750532.231 * [exit]simplify: Simplified to (/ (sqrt PI) (sqrt (sqrt k))) 1536750532.231 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt PI) (sqrt (sqrt k))) (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))))))) 1536750532.231 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt (sqrt k))) 1536750532.232 * * [misc]simplify: iters left: 6 (9 enodes) 1536750532.235 * * [misc]simplify: iters left: 5 (11 enodes) 1536750532.237 * [exit]simplify: Simplified to (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))) 1536750532.237 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt PI) (sqrt (sqrt k))) (/ (pow PI (/ (- k) 2)) (sqrt (sqrt k))))))) 1536750532.237 * * * * [misc]progress: [ 111 / 144 ] simplifiying candidate # 1536750532.237 * [enter]simplify: Simplifying (/ (pow PI 1/2) 1) 1536750532.238 * * [misc]simplify: iters left: 3 (5 enodes) 1536750532.239 * * [misc]simplify: iters left: 2 (8 enodes) 1536750532.240 * * [misc]simplify: iters left: 1 (10 enodes) 1536750532.241 * [exit]simplify: Simplified to (sqrt PI) 1536750532.241 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt PI) (/ (pow PI (- (/ k 2))) (sqrt k)))))) 1536750532.242 * [enter]simplify: Simplifying (/ (pow PI (- (/ k 2))) (sqrt k)) 1536750532.242 * * [misc]simplify: iters left: 6 (8 enodes) 1536750532.244 * * [misc]simplify: iters left: 5 (10 enodes) 1536750532.245 * [exit]simplify: Simplified to (/ (pow PI (- (/ k 2))) (sqrt k)) 1536750532.245 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt PI) (/ (pow PI (- (/ k 2))) (sqrt k)))))) 1536750532.245 * * * * [misc]progress: [ 112 / 144 ] simplifiying candidate # 1536750532.246 * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750532.246 * * [misc]simplify: iters left: 6 (13 enodes) 1536750532.249 * * [misc]simplify: iters left: 5 (21 enodes) 1536750532.254 * * [misc]simplify: iters left: 4 (33 enodes) 1536750532.261 * * [misc]simplify: iters left: 3 (36 enodes) 1536750532.272 * * [misc]simplify: iters left: 2 (39 enodes) 1536750532.287 * [exit]simplify: Simplified to (* (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) 1536750532.288 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (* (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))) 1536750532.288 * [enter]simplify: Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750532.289 * * [misc]simplify: iters left: 6 (11 enodes) 1536750532.293 * * [misc]simplify: iters left: 5 (13 enodes) 1536750532.297 * * [misc]simplify: iters left: 4 (16 enodes) 1536750532.305 * [exit]simplify: Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750532.305 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))) 1536750532.305 * * * * [misc]progress: [ 113 / 144 ] simplifiying candidate # 1536750532.305 * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1536750532.307 * * [misc]simplify: iters left: 6 (12 enodes) 1536750532.311 * * [misc]simplify: iters left: 5 (16 enodes) 1536750532.317 * * [misc]simplify: iters left: 4 (21 enodes) 1536750532.323 * * [misc]simplify: iters left: 3 (22 enodes) 1536750532.332 * [exit]simplify: Simplified to (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k))) 1536750532.332 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))) 1536750532.332 * [enter]simplify: Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750532.333 * * [misc]simplify: iters left: 6 (11 enodes) 1536750532.335 * * [misc]simplify: iters left: 5 (13 enodes) 1536750532.337 * * [misc]simplify: iters left: 4 (16 enodes) 1536750532.340 * [exit]simplify: Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750532.340 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))) 1536750532.340 * * * * [misc]progress: [ 114 / 144 ] simplifiying candidate # 1536750532.340 * [enter]simplify: Simplifying (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1) 1536750532.340 * * [misc]simplify: iters left: 6 (11 enodes) 1536750532.343 * * [misc]simplify: iters left: 5 (17 enodes) 1536750532.346 * * [misc]simplify: iters left: 4 (26 enodes) 1536750532.350 * * [misc]simplify: iters left: 3 (28 enodes) 1536750532.353 * * [misc]simplify: iters left: 2 (33 enodes) 1536750532.358 * [exit]simplify: Simplified to (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1536750532.358 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)))))) 1536750532.358 * [enter]simplify: Simplifying (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536750532.359 * * [misc]simplify: iters left: 6 (10 enodes) 1536750532.361 * * [misc]simplify: iters left: 5 (12 enodes) 1536750532.363 * * [misc]simplify: iters left: 4 (15 enodes) 1536750532.367 * [exit]simplify: Simplified to (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536750532.367 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (/ (cbrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)))))) 1536750532.367 * * * * [misc]progress: [ 115 / 144 ] simplifiying candidate # 1536750532.368 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750532.369 * * [misc]simplify: iters left: 6 (12 enodes) 1536750532.373 * * [misc]simplify: iters left: 5 (16 enodes) 1536750532.377 * * [misc]simplify: iters left: 4 (19 enodes) 1536750532.380 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750532.381 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))) 1536750532.381 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750532.381 * * [misc]simplify: iters left: 6 (11 enodes) 1536750532.383 * * [misc]simplify: iters left: 5 (13 enodes) 1536750532.385 * * [misc]simplify: iters left: 4 (16 enodes) 1536750532.388 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))) 1536750532.388 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))) 1536750532.388 * * * * [misc]progress: [ 116 / 144 ] simplifiying candidate # 1536750532.388 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750532.389 * * [misc]simplify: iters left: 6 (11 enodes) 1536750532.391 * * [misc]simplify: iters left: 5 (13 enodes) 1536750532.393 * * [misc]simplify: iters left: 4 (16 enodes) 1536750532.396 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750532.396 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))) 1536750532.397 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750532.398 * * [misc]simplify: iters left: 6 (11 enodes) 1536750532.400 * * [misc]simplify: iters left: 5 (13 enodes) 1536750532.402 * * [misc]simplify: iters left: 4 (16 enodes) 1536750532.406 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) 1536750532.406 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))) 1536750532.406 * * * * [misc]progress: [ 117 / 144 ] simplifiying candidate # 1536750532.407 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) 1) 1536750532.408 * * [misc]simplify: iters left: 6 (10 enodes) 1536750532.411 * * [misc]simplify: iters left: 5 (14 enodes) 1536750532.417 * * [misc]simplify: iters left: 4 (19 enodes) 1536750532.421 * [exit]simplify: Simplified to (sqrt (pow PI (- 1/2 (/ k 2)))) 1536750532.421 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)))))) 1536750532.421 * [enter]simplify: Simplifying (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536750532.421 * * [misc]simplify: iters left: 6 (10 enodes) 1536750532.423 * * [misc]simplify: iters left: 5 (12 enodes) 1536750532.425 * * [misc]simplify: iters left: 4 (15 enodes) 1536750532.428 * [exit]simplify: Simplified to (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)) 1536750532.428 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (sqrt k)))))) 1536750532.428 * * * * [misc]progress: [ 118 / 144 ] simplifiying candidate # 1536750532.428 * [enter]simplify: Simplifying (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) 1536750532.428 * * [misc]simplify: iters left: 6 (6 enodes) 1536750532.429 * * [misc]simplify: iters left: 5 (10 enodes) 1536750532.431 * [exit]simplify: Simplified to (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) 1536750532.431 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))))))) 1536750532.432 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750532.432 * * [misc]simplify: iters left: 6 (10 enodes) 1536750532.434 * * [misc]simplify: iters left: 5 (12 enodes) 1536750532.436 * * [misc]simplify: iters left: 4 (15 enodes) 1536750532.439 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))) 1536750532.439 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))))))) 1536750532.439 * * * * [misc]progress: [ 119 / 144 ] simplifiying candidate # 1536750532.439 * [enter]simplify: Simplifying (/ 1 (sqrt (sqrt k))) 1536750532.439 * * [misc]simplify: iters left: 4 (5 enodes) 1536750532.440 * * [misc]simplify: iters left: 3 (7 enodes) 1536750532.441 * [exit]simplify: Simplified to (/ 1 (sqrt (sqrt k))) 1536750532.441 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))))) 1536750532.441 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750532.442 * * [misc]simplify: iters left: 6 (10 enodes) 1536750532.444 * * [misc]simplify: iters left: 5 (12 enodes) 1536750532.445 * * [misc]simplify: iters left: 4 (15 enodes) 1536750532.448 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) 1536750532.448 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* (/ 1 (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))))) 1536750532.448 * * * * [misc]progress: [ 120 / 144 ] simplifiying candidate # 1536750532.448 * [enter]simplify: Simplifying (/ 1 1) 1536750532.448 * * [misc]simplify: iters left: 2 (2 enodes) 1536750532.449 * * [misc]simplify: iters left: 1 (4 enodes) 1536750532.449 * [exit]simplify: Simplified to 1 1536750532.449 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* 1 (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536750532.449 * [enter]simplify: Simplifying (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536750532.450 * * [misc]simplify: iters left: 6 (9 enodes) 1536750532.451 * * [misc]simplify: iters left: 5 (11 enodes) 1536750532.453 * * [misc]simplify: iters left: 4 (14 enodes) 1536750532.455 * [exit]simplify: Simplified to (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)) 1536750532.455 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (* 1 (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))) 1536750532.456 * * * * [misc]progress: [ 121 / 144 ] simplifiying candidate # 1536750532.456 * * * * [misc]progress: [ 122 / 144 ] simplifiying candidate # 1536750532.456 * * * * [misc]progress: [ 123 / 144 ] simplifiying candidate # 1536750532.456 * * * * [misc]progress: [ 124 / 144 ] simplifiying candidate # 1536750532.456 * [enter]simplify: Simplifying (cbrt (sqrt k)) 1536750532.456 * * [misc]simplify: iters left: 2 (3 enodes) 1536750532.457 * [exit]simplify: Simplified to (cbrt (sqrt k)) 1536750532.457 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))))) 1536750532.457 * * * * [misc]progress: [ 125 / 144 ] simplifiying candidate # 1536750532.457 * [enter]simplify: Simplifying (sqrt (sqrt k)) 1536750532.457 * * [misc]simplify: iters left: 2 (3 enodes) 1536750532.458 * [exit]simplify: Simplified to (sqrt (sqrt k)) 1536750532.458 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k)))))) 1536750532.458 * * * * [misc]progress: [ 126 / 144 ] simplifiying candidate # 1536750532.458 * [enter]simplify: Simplifying (sqrt k) 1536750532.458 * * [misc]simplify: iters left: 1 (2 enodes) 1536750532.458 * [exit]simplify: Simplified to (sqrt k) 1536750532.458 * [misc]simplify: Simplified (2 2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (/ (pow PI (- 1/2 (/ k 2))) 1) (sqrt k))))) 1536750532.458 * * * * [misc]progress: [ 127 / 144 ] simplifiying candidate # 1536750532.458 * [enter]simplify: Simplifying (pow PI 1/2) 1536750532.459 * * [misc]simplify: iters left: 1 (3 enodes) 1536750532.459 * [exit]simplify: Simplified to (sqrt PI) 1536750532.459 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (sqrt PI) (/ (sqrt k) (pow PI (- (/ k 2)))))))) 1536750532.459 * * * * [misc]progress: [ 128 / 144 ] simplifiying candidate # 1536750532.459 * [enter]simplify: Simplifying (pow PI 1/2) 1536750532.460 * * [misc]simplify: iters left: 1 (3 enodes) 1536750532.460 * [exit]simplify: Simplified to (sqrt PI) 1536750532.460 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (sqrt PI) (/ (sqrt k) (pow PI (- (/ k 2)))))))) 1536750532.460 * * * * [misc]progress: [ 129 / 144 ] simplifiying candidate # 1536750532.460 * [enter]simplify: Simplifying (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1536750532.461 * * [misc]simplify: iters left: 6 (9 enodes) 1536750532.462 * * [misc]simplify: iters left: 5 (11 enodes) 1536750532.464 * * [misc]simplify: iters left: 4 (14 enodes) 1536750532.467 * [exit]simplify: Simplified to (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) 1536750532.467 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (* (cbrt (pow PI (- 1/2 (/ k 2)))) (cbrt (pow PI (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow PI (- 1/2 (/ k 2))))))))) 1536750532.467 * * * * [misc]progress: [ 130 / 144 ] simplifiying candidate # 1536750532.467 * [enter]simplify: Simplifying (sqrt (pow PI (- 1/2 (/ k 2)))) 1536750532.467 * * [misc]simplify: iters left: 6 (8 enodes) 1536750532.469 * * [misc]simplify: iters left: 5 (10 enodes) 1536750532.471 * * [misc]simplify: iters left: 4 (13 enodes) 1536750532.473 * [exit]simplify: Simplified to (sqrt (pow PI (- 1/2 (/ k 2)))) 1536750532.473 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (sqrt (pow PI (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow PI (- 1/2 (/ k 2))))))))) 1536750532.473 * * * * [misc]progress: [ 131 / 144 ] simplifiying candidate # 1536750532.473 * * * * [misc]progress: [ 132 / 144 ] simplifiying candidate # 1536750532.473 * [enter]simplify: Simplifying (pow PI 1/2) 1536750532.473 * * [misc]simplify: iters left: 1 (3 enodes) 1536750532.474 * [exit]simplify: Simplified to (sqrt PI) 1536750532.474 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (sqrt PI) (* (sqrt k) (pow PI (/ k 2))))))) 1536750532.474 * * * * [misc]progress: [ 133 / 144 ] simplifiying candidate # 1536750532.474 * [enter]simplify: Simplifying (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 1536750532.475 * * [misc]simplify: iters left: 6 (18 enodes) 1536750532.482 * * [misc]simplify: iters left: 5 (39 enodes) 1536750532.504 * * [misc]simplify: iters left: 4 (104 enodes) 1536750532.553 * * [misc]simplify: iters left: 3 (275 enodes) 1536750532.734 * [exit]simplify: Simplified to (+ (* (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8)) (+ (* (* k (log PI)) (* (sqrt PI) -1/2)) (sqrt PI))) 1536750532.734 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (+ (* (* (* k (log PI)) (* k (log PI))) (* (sqrt PI) 1/8)) (+ (* (* k (log PI)) (* (sqrt PI) -1/2)) (sqrt PI))) (sqrt k))))) 1536750532.734 * * * * [misc]progress: [ 134 / 144 ] simplifiying candidate # 1536750532.734 * [enter]simplify: Simplifying (pow PI (- 1/2 (* 1/2 k))) 1536750532.734 * * [misc]simplify: iters left: 5 (6 enodes) 1536750532.736 * * [misc]simplify: iters left: 4 (9 enodes) 1536750532.738 * * [misc]simplify: iters left: 3 (17 enodes) 1536750532.743 * * [misc]simplify: iters left: 2 (20 enodes) 1536750532.748 * * [misc]simplify: iters left: 1 (24 enodes) 1536750532.760 * [exit]simplify: Simplified to (pow PI (- 1/2 (* k 1/2))) 1536750532.760 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (* k 1/2))) (sqrt k))))) 1536750532.760 * * * * [misc]progress: [ 135 / 144 ] simplifiying candidate # 1536750532.761 * [enter]simplify: Simplifying (pow PI (- 1/2 (* 1/2 k))) 1536750532.761 * * [misc]simplify: iters left: 5 (6 enodes) 1536750532.764 * * [misc]simplify: iters left: 4 (9 enodes) 1536750532.768 * * [misc]simplify: iters left: 3 (17 enodes) 1536750532.772 * * [misc]simplify: iters left: 2 (20 enodes) 1536750532.775 * * [misc]simplify: iters left: 1 (24 enodes) 1536750532.781 * [exit]simplify: Simplified to (pow PI (- 1/2 (* k 1/2))) 1536750532.781 * [misc]simplify: Simplified (2 2 2 1) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (* k 1/2))) (sqrt k))))) 1536750532.781 * * * * [misc]progress: [ 136 / 144 ] simplifiying candidate # 1536750532.781 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 1536750532.781 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536750532.781 * * * * [misc]progress: [ 137 / 144 ] simplifiying candidate # 1536750532.782 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2)))))))) 1536750532.782 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536750532.782 * * * * [misc]progress: [ 138 / 144 ] simplifiying candidate # 1536750532.782 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k))))))) 1536750532.782 * [misc]simplify: Simplified (2) to (λ (k n) +nan.0) 1536750532.782 * * * * [misc]progress: [ 139 / 144 ] simplifiying candidate # 1536750532.782 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (pow k 2)))) (- (+ (* +nan.0 (sqrt (* n PI))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log PI) 2) (pow k 2)))) (- (+ (* +nan.0 (* (sqrt (* n PI)) k)) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log n) k))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (log PI) k))) (- (+ (* +nan.0 (* (sqrt (* n PI)) (* (pow (log n) 2) (pow k 2)))) (- (* +nan.0 (* (sqrt (* n PI)) (pow k 2)))))))))))))))))))))) 1536750532.782 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0)) 1536750532.782 * * * * [misc]progress: [ 140 / 144 ] simplifiying candidate # 1536750532.782 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 1536750532.782 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0)) 1536750532.782 * * * * [misc]progress: [ 141 / 144 ] simplifiying candidate # 1536750532.783 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))))))))) 1536750532.783 * [misc]simplify: Simplified (2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) +nan.0)) 1536750532.783 * * * * [misc]progress: [ 142 / 144 ] simplifiying candidate # 1536750532.783 * [enter]simplify: Simplifying (- (+ (* +nan.0 (* (* (log PI) k) (sqrt PI))) (- (+ (* +nan.0 (* (sqrt PI) k)) (- (+ (* +nan.0 (* (sqrt PI) (pow k 2))) (- (+ (* +nan.0 (* (* (log PI) (pow k 2)) (sqrt PI))) (- (+ (* +nan.0 (sqrt PI)) (- (* +nan.0 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))))))))))))) 1536750532.783 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) +nan.0))) 1536750532.783 * * * * [misc]progress: [ 143 / 144 ] simplifiying candidate # 1536750532.783 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) k)) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 3))) (- (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 2)))))))) 1536750532.783 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) +nan.0))) 1536750532.783 * * * * [misc]progress: [ 144 / 144 ] simplifiying candidate # 1536750532.783 * [enter]simplify: Simplifying (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) k)) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (pow k 2))) (- (* +nan.0 (pow PI (- 1/2 (* 1/2 k))))))))) 1536750532.783 * [misc]simplify: Simplified (2 2 2) to (λ (k n) (* (pow 2 (- 1/2 (/ k 2))) (* (pow n (- 1/2 (/ k 2))) +nan.0))) 1536750532.783 * * * [misc]progress: adding candidates to table 1536750536.096 * [misc]progress: [Phase 3 of 3] Extracting. 1536750536.096 * * [misc]regime: Finding splitpoints for: (# # # # # # # #) 1536750536.102 * * * [misc]regime-changes: Trying 2 branch expressions: (n k) 1536750536.102 * * * * [misc]regimes: Trying to branch on n from (# # # # # # # #) 1536750536.185 * * * * [misc]regimes: Trying to branch on k from (# # # # # # # #) 1536750536.267 * * * [misc]regime: Found split indices: #